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0,999…

2008-11-20T15:43:12Z

Simetrical: /* Digit manipulation */ Remove a minor variation of the exact same thing, which adds no extra info.

[[Image:999 Perspective.png|300px|right]]

In [[mathematics]], the [[recurring decimal]] '''0.999…''', which is also written as <math>0.\bar{9} , 0.\dot{9}</math> or <math> 0.(9)\,\!</math>, denotes a [[real number]] [[equality (mathematics)|equal]] to [[1 (number)|1]]. In other words, the notations "0.999…" and "1" represent the same real number. The [[Equality (mathematics)|equality]] has long been accepted by professional mathematicians and taught in textbooks. Various [[mathematical proof|proofs]] of this identity have been formulated with various degrees of [[mathematical rigour]], preferred development of the real numbers, background assumptions, historical context, and target audience.

The non-uniqueness of real expansions such as 0.999… is not limited to the decimal system. The same phenomenon occurs in all [[integer]] [[radix|base]]s, and mathematicians have also quantified the ways of writing 1 in [[Non-integer representation|non-integer bases]]. Nor is this phenomenon unique to 1: every non-zero, terminating decimal has a twin with trailing 9s, such as 28.3287 and 28.3286999…. For simplicity, the terminating decimal is almost always the preferred representation, contributing to a misconception that it is the ''only'' representation. Even more generally, any [[positional numeral system]] contains infinitely many numbers with multiple representations. These various identities have been applied to better understand patterns in the decimal expansions of [[fraction (mathematics)|fraction]]s and the structure of a simple [[fractal]], the [[Cantor set]]. They also occur in a classic investigation of the infinitude of the entire set of real numbers.

In the last few decades, researchers of [[mathematics education]] have studied the reception of this equality among students, many of whom initially question or reject this equality. Many are persuaded by textbooks, teachers and arithmetic reasoning as below to accept that the two are equal. However, they are often uneasy enough that they offer further justification. The students' reasoning for denying or affirming the equality is typically based on one of a few common [[erroneous intuitions]] about the real numbers; for example that each real number has a unique [[decimal expansion]], that nonzero [[infinitesimal]] real numbers should exist, or that the expansion of 0.999… eventually terminates. Number systems that bear out some of these intuitions can be constructed, but only outside the standard [[real number]] system used in elementary, and most higher, mathematics. Indeed, some settings contain numbers that are "just shy" of 1; these are generally unrelated to 0.999…, but they are of considerable interest in [[mathematical analysis]].

==Introduction==
0.999… is a number written in the [[decimal]] [[numeral system]], and some of the simplest proofs that 0.999… = 1 rely on the convenient [[arithmetic]] properties of this system. Most of decimal arithmetic—[[addition]], [[subtraction]], [[multiplication]], [[division (mathematics)|division]], and [[inequality|comparison]]—uses manipulations at the digit level that are much the same as those for [[integer]]s. As with integers, any two ''finite'' decimals with different digits mean different numbers (ignoring trailing zeros). In particular, any number of the form 0.99…9, where the 9s eventually stop, is strictly less than 1.

Misinterpreting the meaning of the use of the "…" ([[ellipsis]]) in 0.999… accounts for some of the misunderstanding about its equality to 1. The use here is different from the usage in language or in 0.99…9, in which the ellipsis specifies that some ''finite'' portion is left unstated or otherwise omitted. When used to specify a [[recurring decimal]], "…" means that some ''infinite'' portion is left unstated, which can only be interpreted as a number by using the mathematical concept of [[limit (mathematics)|limit]]s. As a result, in conventional mathematical usage, the value assigned to the notation "0.999…" is the [[real number]] which is the limit of the [[convergent sequence]] (0.9, 0.99, 0.999, 0.9999, …).

Unlike the case with integers and finite decimals, other notations can also express a single number in multiple ways. For example, using [[Fraction (mathematics)|fraction]]s, 1⁄3 = 2⁄6. Infinite decimals, however, can express the same number in at most two different ways. If there are two ways, then one of them must end with an infinite series of nines, and the other must terminate (that is, consist of a recurring series of zeros from a certain point on).

There are many proofs that 0.999… = 1, of varying degrees of [[mathematical rigour]]. A short sketch of one rigorous proof can be simply stated as follows. Consider that two [[real number]]s are identical [[if and only if]] their difference is equal to zero. Most people would agree that the difference between 0.999… and 1, if it exists at all, must be very small. By considering the convergence of the sequence above, we can show that the magnitude of this difference must be smaller than any positive quantity, and it can be shown (see [[Archimedean property]] for details) that the only real number with this property is 0. Since the difference is 0 it follows that the numbers 1 and 0.999… are identical. The same argument also explains why 0.333… = 1⁄3, 0.111… = 1⁄9, etc.

==Proofs==
===Algebraic===
==== Fractions ====

One reason that infinite decimals are a necessary extension of finite decimals is to represent fractions. Using [[long division]], a simple division of integers like 1⁄3 becomes a recurring decimal, 0.333…, in which the digits repeat without end. This decimal yields a quick proof for 0.999… = 1. Multiplication of 3 times 3 produces 9 in each digit, so 3 × 0.333… equals 0.999…. And 3 × 1⁄3 equals 1, so 0.999… = 1.<ref name="CME">cf. with the binary version of the same argument in [[Silvanus P. Thompson]], ''Calculus made easy'', St. Martin's Press, New York, 1998. ISBN 0-312-18548-0.</ref>

Another form of this proof multiplies 1/9 = 0.111… by 9.

:{| style="wikitable"
|<math>
\begin{align}
0.333\dots &{} = \frac{1}{3} \\
3 \times 0.333\dots &{} = 3 \times \frac{1}{3} = \frac{3 \times 1}{3} \\
0.999\dots &{} = 1
\end{align}
</math>
|width="25px"|
|width="25px" style="border-left:1px solid silver;"|
|<math>
\begin{align}
0.111\dots & {} = \frac{1}{9} \\
9 \times 0.111\dots & {} = 9 \times \frac{1}{9} = \frac{9 \times 1}{9} \\
0.999\dots & {} = 1
\end{align}
</math>
|}

An even easier version of the same proof is based on the following equations:

:<math>
1 = \frac{9}{9} = 9 \times \frac{1}{9} = 9 \times 0.111\dots = 0.999\dots
</math>

Since both equations are valid, by the [[transitive property]], 0.999… must equal 1. Similarly, 3/3 = 1, and 3/3 = 0.999…. So, 0.999… must equal 1.

==== Digit manipulation ====

Another kind of proof more easily adapts to other repeating decimals. When a number in decimal notation is multiplied by 10, the digits do not change but the decimal separator moves one place to the right. Thus 10 × 0.999… equals 9.999…, which is 9 greater than the original number.

To see this, consider that subtracting 0.999… from 9.999… can proceed digit by digit; in each of the digits after the decimal separator the result is 9 − 9, which is 0. But trailing zeros do not change a number, so the difference is exactly 9. The final step uses algebra. Let the decimal number in question, 0.999…, be called ''x''. Then 10''x'' − ''x'' = 9. This is the same as 9''x'' = 9. Dividing both sides by 9 completes the proof: ''x'' = 1.<ref name="CME"/> Written as a sequence of equations,

:<math>
\begin{align}
x &= 0.999\ldots \\
10 x &= 9.999\ldots \\
10 x - x &= 9.999\ldots - 0.999\ldots \\
9 x &= 9 \\
x &= 1 \\
0.999\ldots &= 1
\end{align}
</math>

The validity of the digit manipulations in the above two proofs does not have to be taken on faith or as an axiom; it follows from the fundamental relationship between decimals and the numbers they represent. This relationship, which can be developed in several equivalent manners, already establishes that the decimals 0.999… and 1.000... both represent the same number.

=== Analytic ===
Since the question of 0.999… does not affect the formal development of mathematics, it can be postponed until one proves the standard theorems of [[real analysis]]. One requirement is to characterize real numbers that can be written in decimal notation, consisting of an optional sign, a finite sequence of any number of digits forming an integer part, a decimal separator, and a sequence of digits forming a fractional part. For the purpose of discussing 0.999…, the integer part can be summarized as ''b''0 and one can neglect negatives, so a decimal expansion has the form
:<math>b_0.b_1b_2b_3b_4b_5\dots</math>

It is vital that the fraction part, unlike the integer part, is not limited to a finite number of digits. This is a [[positional notation]], so for example the 5 in 500 contributes ten times as much as the 5 in 50, and the 5 in 0.05 contributes one tenth as much as the 5 in 0.5.

====Infinite series and sequences====
{{further|[[Decimal representation]]}}

Perhaps the most common development of decimal expansions is to define them as sums of [[infinite series]]. In general:
:<math>b_0 . b_1 b_2 b_3 b_4 \ldots = b_0 + b_1({\tfrac{1}{10}}) + b_2({\tfrac{1}{10}})^2 + b_3({\tfrac{1}{10}})^3 + b_4({\tfrac{1}{10}})^4 + \cdots .</math>

For 0.999… one can apply the powerful [[convergent series|convergence]] theorem concerning [[geometric series]]:<ref>Rudin p.61, Theorem 3.26; J. Stewart p.706</ref>
:If <math>|r| < 1</math> then <math>ar+ar^2+ar^3+\cdots = \frac{ar}{1-r}.</math>

Since 0.999… is such a sum with a common ratio <math>r=\textstyle\frac{1}{10}</math>, the theorem makes short work of the question:
:<math>0.999\ldots = 9(\tfrac{1}{10}) + 9({\tfrac{1}{10}})^2 + 9({\tfrac{1}{10}})^3 + \cdots = \frac{9({\tfrac{1}{10}})}{1-{\tfrac{1}{10}}} = 1.\,</math>
This proof (actually, that 10 equals 9.999…) appears as early as 1770 in [[Leonhard Euler]]'s ''[[Elements of Algebra]]''.<ref>Euler p.170</ref>

[[Image:base4 333.svg|left|thumb|200px|Limits: The unit interval, including the '''base-4''' decimal sequence (.3, .33, .333, …) converging to 1.]]
The sum of a geometric series is itself a result even older than Euler. A typical 18th-century derivation used a term-by-term manipulation similar to the [[#Algebra|algebra proof]] given above, and as late as 1811, Bonnycastle's textbook ''An Introduction to Algebra'' uses such an argument for geometric series to justify the same maneuver on 0.999….<ref>Grattan-Guinness p.69; Bonnycastle p.177</ref> A 19th-century reaction against such liberal summation methods resulted in the definition that still dominates today: the sum of a series is ''defined'' to be the limit of the sequence of its partial sums. A corresponding proof of the theorem explicitly computes that sequence; it can be found in any proof-based introduction to calculus or analysis.<ref>For example, J. Stewart p.706, Rudin p.61, Protter and Morrey p.213, Pugh p.180, J.B. Conway p.31</ref>

A [[sequence]] (''x''0, ''x''1, ''x''2, …) has a [[limit of a sequence|limit]] ''x'' if the distance |''x'' − ''x''''n''| becomes arbitrarily small as ''n'' increases. The statement that 0.999… = 1 can itself be interpreted and proven as a limit:
:<math>0.999\ldots = \lim_{n\to\infty}0.\underbrace{ 99\ldots9 }_{n} = \lim_{n\to\infty}\sum_{k = 1}^n\frac{9}{10^k} = \lim_{n\to\infty}\left(1-\frac{1}{10^n}\right) = 1-\lim_{n\to\infty}\frac{1}{10^n} = 1.\,</math><ref>The limit follows, for example, from Rudin p. 57, Theorem 3.20e. For a more direct approach, see also Finney, Weir, Giordano (2001) ''Thomas' Calculus: Early Transcendentals'' 10ed, Addison-Wesley, New York. Section 8.1, example 2(a), example 6(b).</ref>

The last step — that <math>\lim_{n\to\infty} \frac{1}{10^n} = 0</math> — is often justified by the axiom that the real numbers have the [[Archimedean property]]. This limit-based attitude towards 0.999… is often put in more evocative but less precise terms. For example, the 1846 textbook ''The University Arithmetic'' explains, ".999 +, continued to infinity = 1, because every annexation of a 9 brings the value closer to 1"; the 1895 ''Arithmetic for Schools'' says, "…when a large number of 9s is taken, the difference between 1 and .99999… becomes inconceivably small".<ref>Davies p.175; Smith and Harrington p.115</ref> Such [[heuristic]]s are often interpreted by students as implying that 0.999… itself is less than 1.

====Nested intervals and least upper bounds====
{{further|[[Nested intervals]]}}

[[Image:999 Intervals C.svg|right|thumb|250px|Nested intervals: in base 3, 1 = 1.000… = 0.222…]]
The series definition above is a simple way to define the real number named by a decimal expansion. A complementary approach is tailored to the opposite process: for a given real number, define the decimal expansion(s) to name it.

If a real number ''x'' is known to lie in the [[closed interval]] [0, 10] (i.e., it is greater than or equal to 0 and less than or equal to 10), one can imagine dividing that interval into ten pieces that overlap only at their endpoints: [0, 1], [1, 2], [2, 3], and so on up to [9, 10]. The number ''x'' must belong to one of these; if it belongs to [2, 3] then one records the digit "2" and subdivides that interval into [2, 2.1], [2.1, 2.2], …, [2.8, 2.9], [2.9, 3]. Continuing this process yields an infinite sequence of [[nested intervals]], labeled by an infinite sequence of digits ''b''0, ''b''1, ''b''2, ''b''3, …, and one writes
:''x'' = ''b''0.''b''1''b''2''b''3…

In this formalism, the identities 1 = 0.999… and 1 = 1.000… reflect, respectively, the fact that 1 lies in both [0, 1] and [1, 2], so one can choose either subinterval when finding its digits. To ensure that this notation does not abuse the "=" sign, one needs a way to reconstruct a unique real number for each decimal. This can be done with limits, but other constructions continue with the ordering theme.<ref>Beals p.22; I. Stewart p.34</ref>

One straightforward choice is the [[nested intervals theorem]], which guarantees that given a sequence of nested, closed intervals whose lengths become arbitrarily small, the intervals contain exactly one real number in their [[intersection (set theory)|intersection]]. So ''b''0.''b''1''b''2''b''3… is defined to be the unique number contained within all the intervals [''b''0, ''b''0 + 1], [''b''0.''b''1, ''b''0.''b''1 + 0.1], and so on. 0.999… is then the unique real number that lies in all of the intervals [0, 1], [0.9, 1], [0.99, 1], and [0.99…9, 1] for every finite string of 9s. Since 1 is an element of each of these intervals, 0.999… = 1.<ref>Bartle and Sherbert pp.60–62; Pedrick p.29; Sohrab p.46</ref>

The Nested Intervals Theorem is usually founded upon a more fundamental characteristic of the real numbers: the existence of [[least upper bound]]s or ''suprema''. To directly exploit these objects, one may define ''b''0.''b''1''b''2''b''3… to be the least upper bound of the set of approximants {''b''0, ''b''0.''b''1, ''b''0.''b''1''b''2, …}.<ref>Apostol pp.9, 11–12; Beals p.22; Rosenlicht p.27</ref> One can then show that this definition (or the nested intervals definition) is consistent with the subdivision procedure, implying 0.999… = 1 again. Tom Apostol concludes,
<blockquote>
The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum.<ref>Apostol p.12</ref>
</blockquote>

=== Based on the construction of the real numbers ===
{{further|[[Construction of the real numbers]]}}

Some approaches explicitly define real numbers to be certain [[construction of the real numbers|structures built upon the rational numbers]], using [[axiomatic set theory]]. The [[natural number]]s — 0, 1, 2, 3, and so on — begin with 0 and continue upwards, so that every number has a successor. One can extend the natural numbers with their negatives to give all the [[integer]]s, and to further extend to ratios, giving the [[rational number]]s. These number systems are accompanied by the arithmetic of addition, subtraction, multiplication, and division. More subtly, they include [[order theory|ordering]], so that one number can be compared to another and found less than, greater than, or equal.

The step from rationals to reals is a major extension. There are at least two popular ways to achieve this step, both published in 1872: [[Dedekind cut]]s and [[Cauchy sequence]]s. Proofs that 0.999… = 1 which directly use these constructions are not found in textbooks on real analysis, where the modern trend for the last few decades has been to use an axiomatic analysis. Even when a construction is offered, it is usually applied towards proving the axioms of the real numbers, which then support the above proofs. However, several authors express the idea that starting with a construction is more logically appropriate, and the resulting proofs are more self-contained.<ref>The historical synthesis is claimed by Griffiths and Hilton (p.xiv) in 1970 and again by Pugh (p.10) in 2001; both actually prefer Dedekind cuts to axioms. For the use of cuts in textbooks, see Pugh p.17 or Rudin p.17. For viewpoints on logic, Pugh p.10, Rudin p.ix, or Munkres p.30</ref>

==== Dedekind cuts ====
{{further|[[Dedekind cut]]}}

In the [[Dedekind cut]] approach, each real number ''x'' is defined as the [[infinite set]] of all rational numbers that are less than ''x''.<ref>Enderton (p.113) qualifies this description: "The idea behind Dedekind cuts is that a real number ''x'' can be named by giving an infinite set of rationals, namely all the rationals less than ''x''. We will in effect define ''x'' to be the set of rationals smaller than ''x''. To avoid circularity in the definition, we must be able to characterize the sets of rationals obtainable in this way…"</ref> In particular, the real number 1 is the set of all rational numbers that are less than 1.<ref>Rudin pp.17–20, Richman p.399, or Enderton p.119. To be precise, Rudin, Richman, and Enderton call this cut 1*, 1−, and 1''R'', respectively; all three identify it with the traditional real number 1. Note that what Rudin and Enderton call a Dedekind cut, Richman calls a "nonprincipal Dedekind cut".</ref> Every positive decimal expansion easily determines a Dedekind cut: the set of rational numbers which are less than some stage of the expansion. So the real number 0.999… is the set of rational numbers ''r'' such that ''r'' < 0, or ''r'' < 0.9, or ''r'' < 0.99, or ''r'' is less than some other number of the form <math>\begin{align}1-(\tfrac{1}{10})^n\end{align}</math>.<ref>Richman p.399</ref> Every element of 0.999… is less than 1, so it is an element of the real number 1. Conversely, an element of 1 is a rational number
<math>\begin{align}\tfrac{a}{b}<1\end{align}</math>, which implies <math>\begin{align}\tfrac{a}{b}<1-(\tfrac{1}{10})^b\end{align}</math>. Since 0.999… and 1 contain the same rational numbers, they are the same set: 0.999… = 1.

The definition of real numbers as Dedekind cuts was first published by [[Richard Dedekind]] in 1872.<ref name="MacTutor2">{{cite web |url=http://www-gap.dcs.st-and.ac.uk/~history/PrintHT/Real_numbers_2.html |title=History topic: The real numbers: Stevin to Hilbert |author=J J O'Connor and E F Robertson |work=MacTutor History of Mathematics |month=October | year=2005 |accessdate=2006-08-30}}</ref>
The above approach to assigning a real number to each decimal expansion is due to an expository paper titled "Is 0.999 … = 1?" by Fred Richman in ''[[Mathematics Magazine]]'', which is targeted at teachers of collegiate mathematics, especially at the junior/senior level, and their students.<ref>{{cite web |url=http://www.maa.org/pubs/mm-guide.html |title=Mathematics Magazine:Guidelines for Authors |publisher=[[Mathematical Association of America]] |accessdate=2006-08-23}}</ref> Richman notes that taking Dedekind cuts in any [[dense subset]] of the rational numbers yields the same results; in particular, he uses [[decimal fraction]]s, for which the proof is more immediate: "So we see that in the traditional definition of the real numbers, the equation 0.9* = 1 is built in at the beginning."<ref>Richman pp.398–399</ref> A further modification of the procedure leads to a different structure that Richman is more interested in describing; see "[[#Alternative number systems|Alternative number systems]]" below.

==== Cauchy sequences ====
{{further|[[Cauchy sequence]]}}

Another approach to constructing the real numbers uses the ordering of rationals less directly. First, the distance between ''x'' and ''y'' is defined as the absolute value |''x'' − ''y''|, where the absolute value |''z''| is defined as the maximum of ''z'' and −''z'', thus never negative. Then the reals are defined to be the sequences of rationals that have the [[Cauchy sequence]] property using this distance. That is, in the sequence (''x''0, ''x''1, ''x''2, …), a mapping from natural numbers to rationals, for any positive rational δ there is an ''N'' such that |''x''''m'' − ''x''''n''| ≤ δ for all ''m'', ''n'' > ''N''. (The distance between terms becomes smaller than any positive rational.)<ref>Griffiths & Hilton §24.2 "Sequences" p.386</ref>

If (''x''''n'') and (''y''''n'') are two Cauchy sequences, then they are defined to be equal as real numbers if the sequence (''x''''n'' − ''y''''n'') has the limit 0. Truncations of the decimal number ''b''0.''b''1''b''2''b''3… generate a sequence of rationals which is Cauchy; this is taken to define the real value of the number.<ref>Griffiths & Hilton pp.388, 393</ref> Thus in this formalism the task is to show that the sequence of rational numbers
:<math>\left(1 - 0, 1 - {9 \over 10}, 1 - {99 \over 100}, \dots\right)
= \left(1, {1 \over 10}, {1 \over 100}, \dots \right)</math>

has the limit 0. Considering the ''n''th term of the sequence, for ''n''=0,1,2,…, it must therefore be shown that
:<math>\lim_{n\rightarrow\infty}\frac{1}{10^n} = 0.</math>

This limit is plain;<ref>Griffiths & Hilton pp.395</ref> one possible proof is that for ε = ''a''/''b'' > 0 one can take ''N'' = ''b'' in the definition of the [[limit of a sequence]]. So again 0.999… = 1.

The definition of real numbers as Cauchy sequences was first published separately by [[Eduard Heine]] and [[Georg Cantor]], also in 1872.<ref name="MacTutor2" /> The above approach to decimal expansions, including the proof that 0.999… = 1, closely follows Griffiths & Hilton's 1970 work ''A comprehensive textbook of classical mathematics: A contemporary interpretation''. The book is written specifically to offer a second look at familiar concepts in a contemporary light.<ref>Griffiths & Hilton pp.viii, 395</ref>

==Generalizations==
The result that 0.999… = 1 generalizes readily in two ways. First, every nonzero number with a finite decimal notation (equivalently, endless trailing 0s) has a counterpart with trailing 9s. For example, 0.24999… equals 0.25, exactly as in the special case considered. These numbers are exactly the decimal fractions, and they are dense.<ref>Petkovšek p.408</ref>

Second, a comparable theorem applies in each radix or [[base (mathematics)|base]]. For example, in base 2 (the [[binary numeral system]]) 0.111… equals 1, and in base 3 (the [[ternary numeral system]]) 0.222… equals 1. Textbooks of real analysis are likely to skip the example of 0.999… and present one or both of these generalizations from the start.<ref>Protter and Morrey p.503; Bartle and Sherbert p.61</ref>

Alternative representations of 1 also occur in non-integer bases. For example, in the [[golden ratio base]], the two standard representations are 1.000… and 0.101010…, and there are infinitely many more representations that include adjacent 1s. Generally, for [[almost all]] ''q'' between 1 and 2, there are uncountably many base-''q'' expansions of 1. On the other hand, there are still uncountably many ''q'' (including all natural numbers greater than 1) for which there is only one base-''q'' expansion of 1, other than the trivial 1.000…. This result was first obtained by [[Paul Erdős]], Miklos Horváth, and István Joó around 1990. In 1998 Vilmos Komornik and Paola Loreti determined the smallest such base, the [[Komornik-Loreti constant]] ''q'' = 1.787231650…. In this base, 1 = 0.11010011001011010010110011010011…; the digits are given by the [[Thue-Morse sequence]], which does not repeat.<ref>Komornik and Loreti p.636</ref>

A more far-reaching generalization addresses [[non-standard positional numeral systems|the most general positional numeral systems]]. They too have multiple representations, and in some sense the difficulties are even worse. For example:<ref>Kempner p.611; Petkovšek p.409</ref>
*In the [[balanced ternary]] system, 1/2 = 0.111… = 1.111….
*In the [[factoradic]] system, 1 = 1.000… = 0.1234….
Marko Petkovšek has proved that such ambiguities are necessary consequences of using a positional system: for any such system that names all the real numbers, the set of reals with multiple representations is always dense. He calls the proof "an instructive exercise in elementary [[point-set topology]]"; it involves viewing sets of positional values as [[Stone space]]s and noticing that their real representations are given by [[continuous function (topology)|continuous functions]].<ref>Petkovšek pp.410–411</ref>

==Applications==
One application of 0.999… as a representation of 1 occurs in elementary [[number theory]]. In 1802, H. Goodwin published an observation on the appearance of 9s in the repeating-decimal representations of fractions whose denominators are certain [[prime number]]s. Examples include:
*1/7 = 0.142857142857… and 142 + 857 = 999.
*1/73 = 0.0136986301369863… and 0136 + 9863 = 9999.
E. Midy proved a general result about such fractions, now called ''[[Midy's theorem]]'', in 1836. The publication was obscure, and it is unclear if his proof directly involved 0.999…, but at least one modern proof by W. G. Leavitt does. If one can prove that a decimal of the form 0.''b''1''b''2''b''3… is a positive integer, then it must be 0.999…, which is then the source of the 9s in the theorem.<ref>Leavitt 1984 p.301</ref> Investigations in this direction can motivate such concepts as [[greatest common divisor]]s, [[modular arithmetic]], [[Fermat prime]]s, [[order (group theory)|order]] of [[group (mathematics)|group]] elements, and [[quadratic reciprocity]].<ref>Lewittes pp.1–3; Leavitt 1967 pp.669,673; Shrader-Frechette pp.96–98</ref>

[[Image:Cantor base 3.svg|right|thumb|Positions of 1/4, 2/3, and 1 in the Cantor set]]
Returning to real analysis, the base-3 analogue 0.222… = 1 plays a key role in a characterization of one of the simplest [[fractal]]s, the middle-thirds [[Cantor set]]:
*A point in the [[unit interval]] lies in the Cantor set if and only if it can be represented in ternary using only the digits 0 and 2.

The ''n''th digit of the representation reflects the position of the point in the ''n''th stage of the construction. For example, the point ²⁄3 is given the usual representation of 0.2 or 0.2000…, since it lies to the right of the first deletion and to the left of every deletion thereafter. The point 1⁄3 is represented not as 0.1 but as 0.0222…, since it lies to the left of the first deletion and to the right of every deletion thereafter.<ref>Pugh p.97; Alligood, Sauer, and Yorke pp.150–152. Protter and Morrey (p.507) and Pedrick (p.29) assign this description as an exercise.</ref>

Repeating nines also turn up in yet another of Georg Cantor's works. They must be taken into account to construct a valid proof, applying [[Cantor's diagonal argument|his 1891 diagonal argument]] to decimal expansions, of the [[uncountability]] of the unit interval. Such a proof needs to be able to declare certain pairs of real numbers to be different based on their decimal expansions, so one needs to avoid pairs like 0.2 and 0.1999… . A simple method represents all numbers with nonterminating expansions; the opposite method rules out repeating nines.<ref>Maor (p.60) and Mankiewicz (p.151) review the former method; Mankiewicz attributes it to Cantor, but the primary source is unclear. Munkres (p.50) mentions the latter method.</ref> A variant that may be closer to Cantor's original argument actually uses base 2, and by turning base-3 expansions into base-2 expansions, one can prove the uncountability of the Cantor set as well.<ref>Rudin p.50, Pugh p.98</ref>

== Skepticism in education ==
Students of mathematics often reject the equality of 0.999… and 1, for reasons ranging from their disparate appearance to deep misgivings over the [[Limit of a sequence|limit]] concept and disagreements over the nature of [[infinitesimal]]s. There are many common contributing factors to the confusion:
*Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a [[paradox]], which is amplified by the appearance of the seemingly well-understood number 1.<ref>Bunch p.119; Tall and Schwarzenberger p.6. The last suggestion is due to Burrell (p.28): "Perhaps the most reassuring of all numbers is 1.…So it is particularly unsettling when someone tries to pass off 0.9~ as 1."</ref>
*Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".<ref>Tall and Schwarzenberger pp.6–7; Tall 2000 p.221</ref>
*Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.<ref>Tall and Schwarzenberger p.6; Tall 2000 p.221</ref>
*Some students regard 0.999… as having a fixed value which is less than 1 by an [[infinitesimal]] but non-zero amount.
*Some students believe that the value of a [[convergent series]] is at best an approximation, that <math>0.\bar{9} \approx 1</math>.
These ideas are mistaken in the context of the standard real numbers, although some may be valid in other number systems, either invented for their general mathematical utility or as instructive [[counterexample]]s to better understand 0.999….

Many of these explanations were found by professor David Tall, who has studied characteristics of teaching and cognition that lead to some of the misunderstandings he has encountered in his college students. Interviewing his students to determine why the vast majority initially rejected the equality, he found that "students continued to conceive of 0.999… as a sequence of numbers getting closer and closer to 1 and not a fixed value, because 'you haven’t specified how many places there are' or 'it is the nearest possible decimal below 1'".<ref>Tall 2000 p.221</ref>

Of the elementary proofs, multiplying 0.333… = 1⁄3 by 3 is apparently a successful strategy for convincing reluctant students that 0.999… = 1. Still, when confronted with the conflict between their belief of the first equation and their disbelief of the second, some students either begin to disbelieve the first equation or simply become frustrated.<ref>Tall 1976 pp.10–14</ref> Nor are more sophisticated methods foolproof: students who are fully capable of applying rigorous definitions may still fall back on intuitive images when they are surprised by a result in advanced mathematics, including 0.999…. For example, one real analysis student was able to prove that 0.333… = 1⁄3 using a [[supremum]] definition, but then insisted that 0.999… < 1 based on her earlier understanding of long division.<ref>Pinto and Tall p.5, Edwards and Ward pp.416–417</ref> Others still are able to prove that 1⁄3 = 0.333…, but, upon being confronted by the [[#Fractions|fractional proof]], insist that "logic" supersedes the mathematical calculations.

[[Joseph Mazur]] tells the tale of an otherwise brilliant calculus student of his who "challenged almost everything I said in class but never questioned his calculator," and who had come to believe that nine digits are all one needs to do mathematics, including calculating the square root of 23. The student remained uncomfortable with a limiting argument that 9.99… = 10, calling it a "wildly imagined infinite growing process."<ref>Mazur pp.137–141</ref>

As part of Ed Dubinsky's "[[APOS theory]]" of mathematical learning, Dubinsky and his collaborators (2005) propose that students who conceive of 0.999… as a finite, indeterminate string with an infinitely small distance from 1 have "not yet constructed a complete process conception of the infinite decimal". Other students who have a complete process conception of 0.999… may not yet be able to "encapsulate" that process into an "object conception", like the object conception they have of 1, and so they view the process 0.999… and the object 1 as incompatible. Dubinsky ''et al.'' also link this mental ability of encapsulation to viewing 1⁄3 as a number in its own right and to dealing with the set of natural numbers as a whole.<ref>Dubinsky ''et al.'' 261–262</ref>

== In popular culture ==

With the rise of the [[Internet]], debates about 0.999… have escaped the classroom and are commonplace on [[newsgroup]]s and [[message board]]s, including many that nominally have little to do with mathematics. In the newsgroup <tt>[news:sci.math sci.math]</tt>, arguing over 0.999… is a "popular sport", and it is one of the questions answered in its [[FAQ]].<ref>As observed by Richman (p.396). {{cite web |url=http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/ |author=Hans de Vreught | year=1994 | title=sci.math FAQ: Why is 0.9999… = 1? |accessdate=2006-06-29}}</ref> The FAQ briefly covers 1⁄3, multiplication by 10, and limits, and it alludes to Cauchy sequences as well.

A 2003 edition of the general-interest [[newspaper column]] ''[[The Straight Dope]]'' discusses 0.999… via 1⁄3 and limits, saying of misconceptions,
<blockquote>
The lower primate in us still resists, saying: .999~ doesn't really represent a ''number'', then, but a ''process''. To find a number we have to halt the process, at which point the .999~ = 1 thing falls apart.

Nonsense.<ref>{{cite web |url=http://www.straightdope.com/columns/030711.html |title=An infinite question: Why doesn't .999~ = 1? |date=2003-07-11 |author=[[Cecil Adams]] |work=[[The Straight Dope]] |publisher=[[Chicago Reader]] |accessdate=2006-09-06}}</ref>
</blockquote>

''The Straight Dope'' cites a discussion on its own message board that grew out of an unidentified "other message board … mostly about video games". In the same vein, the question of 0.999… proved such a popular topic in the first seven years of [[Blizzard Entertainment]]'s [[Battle.net]] forums that the company issued a "press release" on [[April Fools' Day]] 2004 that it is 1:
<blockquote>
We are very excited to close the book on this subject once and for all. We've witnessed the heartache and concern over whether .999~ does or does not equal 1, and we're proud that the following proof finally and conclusively addresses the issue for our customers.<ref>{{cite web |url=http://www.blizzard.com/press/040401.shtml |title=Blizzard Entertainment Announces .999~ (Repeating) = 1 |work=Press Release |publisher=Blizzard Entertainment |date=2004-04-01 |accessdate=2006-09-03}}</ref>
</blockquote>
Two proofs are then offered, based on limits and multiplication by 10.

== Alternative number systems ==
Although the real numbers form an extremely useful [[number system]], the decision to interpret the phrase "0.999…" as naming a real number is ultimately a convention, and Timothy Gowers argues in ''Mathematics: A Very Short Introduction'' that the resulting identity 0.999… = 1 is a convention as well:
<blockquote>
However, it is by no means an arbitrary convention, because not adopting it forces one either to invent strange new objects or to abandon some of the familiar rules of arithmetic.<ref>Gowers p.60</ref>
</blockquote>
One can define other number systems using different rules or new objects; in some such number systems, the above proofs would need to be reinterpreted and one might find that, in a given number system, 0.999… and 1 might not be identical. However, many number systems are extensions of — rather than independent alternatives to — the real number system, so 0.999… = 1 continues to hold. Even in such number systems, though, it is worthwhile to examine alternative number systems, not only for how 0.999… behaves (if, indeed, a number expressed as "0.999…" is both meaningful and unambiguous), but also for the behavior of related phenomena. If such phenomena differ from those in the real number system, then at least one of the assumptions built into the system must break down.

===Infinitesimals===
{{main|Infinitesimal}}

Some proofs that 0.999… = 1 rely on the [[Archimedean property]] of the standard real numbers: there are no nonzero [[infinitesimal]]s. There are mathematically coherent ordered [[algebraic structure]]s, including various alternatives to standard reals, which are non-Archimedean. The meaning of 0.999… depends on which structure we use. For example, the [[dual number]]s include a new infinitesimal element ε, analogous to the imaginary unit ''i'' in the [[complex number]]s except that ε² = 0. The resulting structure is useful in [[automatic differentiation]]. The dual numbers can be given a [[lexicographic order]], in which case the multiples of ε become non-Archimedean elements.<ref>Berz 439–442</ref> Note, however, that, as an extension of the real numbers, the dual numbers still have 0.999…=1. On a related note, while ε exists in dual numbers, so does ε/2, so ε is not "the smallest positive dual number," and, indeed, as in the reals, no such number exists.

Another way to construct alternatives to standard reals is to use [[topos]] theory and alternative logics rather than [[set theory]] and classical logic (which is a special case). For example, [[smooth infinitesimal analysis]] has infinitesimals with no [[Multiplicative inverse|reciprocal]]s.<ref>{{cite paper|url=http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf|title=An Invitation to Smooth Infinitesimal Analysis|author=John L. Bell |year=2003 |format=PDF |accessdate=2006-06-29}}</ref>

[[Non-standard analysis]] is well-known for including a number system with a full array of infinitesimals (and their inverses) which provide a different, and perhaps more intuitive, approach to [[calculus]].<ref>For a full treatment of non-standard numbers see for example Robinson's ''Non-standard Analysis''.</ref> A.H. Lightstone provided a development of non-standard decimal expansions in 1972 in which every extended real number in (0, 1) has a unique extended decimal expansion: a sequence of digits 0.ddd…;…ddd… indexed by the extended natural numbers. In his formalism, there are two natural extensions of 0.333…, neither of which falls short of 1/3 by an infinitesimal:
:0.333…;…000… does not exist, while
:0.333…;…333… = 1/3 exactly.<ref>Lightstone pp.245–247. He does not explore the possibility repeating 9s in the standard part of an expansion.</ref>

[[Combinatorial game theory]] provides alternative reals as well, with infinite Blue-Red [[Hackenbush]] as one particularly relevant example. In 1974, [[Elwyn Berlekamp]] described a correspondence between Hackenbush strings and binary expansions of real numbers, motivated by the idea of [[data compression]]. For example, the value of the Hackenbush string LRRLRLRL… is 0.0101012… = 1/3. However, the value of LRLLL… (corresponding to 0.111…2) is infinitesimally less than 1. The difference between the two is the [[surreal number]] 1/ω, where ω is the first [[ordinal number|infinite ordinal]]; the relevant game is LRRRR… or 0.000…2.<ref>Berlekamp, Conway, and Guy (pp.79–80, 307–311) discuss 1 and 1/3 and touch on 1/ω. The game for 0.111…2 follows directly from Berlekamp's Rule, and it is discussed by {{cite web |url=http://www.maths.nott.ac.uk/personal/anw/Research/Hack/ |title=Hackenstrings and the 0.999… ≟ 1 FAQ |author=A. N. Walker |year=1999 |accessdate=2006-06-29}}</ref>

===Breaking subtraction===
Another manner in which the proofs might be undermined is if 1 − 0.999… simply does not exist, because subtraction is not always possible. Mathematical structures with an addition operation but not a subtraction operation include [[commutative]] [[semigroup]]s, [[commutative monoid]]s and [[semiring]]s. Richman considers two such systems, designed so that 0.999… < 1.

First, Richman defines a nonnegative ''decimal number'' to be a literal decimal expansion. He defines the [[lexicographical order]] and an addition operation, noting that 0.999… < 1 simply because 0 < 1 in the ones place, but for any nonterminating ''x'', one has 0.999… + ''x'' = 1 + ''x''. So one peculiarity of the decimal numbers is that addition cannot always be cancelled; another is that no decimal number corresponds to 1⁄3. After defining multiplication, the decimal numbers form a positive, totally ordered, commutative semiring.<ref>Richman pp.397–399</ref>

In the process of defining multiplication, Richman also defines another system he calls "cut ''D''", which is the set of Dedekind cuts of decimal fractions. Ordinarily this definition leads to the real numbers, but for a decimal fraction ''d'' he allows both the cut (−∞, ''d'' ) and the "principal cut" (−∞, ''d'' ]. The result is that the real numbers are "living uneasily together with" the decimal fractions. Again 0.999… < 1. There are no positive infinitesimals in cut ''D'', but there is "a sort of negative infinitesimal," 0−, which has no decimal expansion. He concludes that 0.999… = 1 + 0−, while the equation "0.999… + ''x'' = 1"
has no solution.<ref>Richman pp.398–400. Rudin (p.23) assigns this alternative construction (but over the rationals) as the last exercise of Chapter 1.</ref>

===''p''-adic numbers===
{{main|p-adic number}}

When asked about 0.999…, novices often believe there should be a "final 9," believing 1 − 0.999… to be a positive number which they write as "0.000…1". Whether or not that makes sense, the intuitive goal is clear: adding a 1 to the last 9 in 0.999… would carry all the 9s into 0s and leave a 1 in the ones place. Among other reasons, this idea fails because there is no "last 9" in 0.999….<ref>Gardiner p.98; Gowers p.60</ref> However, there is a system that contains an infinite string of 9s including a last 9.

[[Image:4adic 333.svg|right|thumb|200px|The 4-adic integers (black points), including the sequence (3, 33, 333, …) converging to −1. The 10-adic analogue is …999 = −1.]]

The [[p-adic number|''p''-adic number]]s are an alternative number system of interest in [[number theory]]. Like the real numbers, the ''p''-adic numbers can be built from the rational numbers via [[Cauchy sequence]]s; the construction uses a different metric in which 0 is closer to ''p'', and much closer to ''pn'', than it is to 1 . The ''p''-adic numbers form a field for prime ''p'' and a [[ring (mathematics)|ring]] for other ''p'', including 10. So arithmetic can be performed in the ''p''-adics, and there are no infinitesimals.

In the 10-adic numbers, the analogues of decimal expansions run to the left. The 10-adic expansion …999 does have a last 9, and it does not have a first 9. One can add 1 to the ones place, and it leaves behind only 0s after carrying through: 1 + …999 = …000 = 0, and so …999 = −1.<ref name="Fjelstad11">Fjelstad p.11</ref> Another derivation uses a geometric series. The infinite series implied by "…999" does not converge in the real numbers, but it converges in the 10-adics, and so one can re-use the familiar formula:
:<math>\ldots999 = 9 + 9(10) + 9(10)^2 + 9(10)^3 + \cdots = \frac{9}{1-10} = -1.</math><ref>Fjelstad pp.14–15</ref>

(Compare with the series [[#Infinite series and sequences|above]].) A third derivation was invented by a seventh-grader who was doubtful over her teacher's limiting argument that 0.999… = 1 but was inspired to take the multiply-by-10 proof [[#Algebra proof|above]] in the opposite direction: if ''x'' = …999 then 10''x'' =  …990, so 10''x'' = ''x'' − 9, hence ''x'' = −1 again.<ref name="Fjelstad11" />

As a final extension, since 0.999… = 1 (in the reals) and …999 = −1 (in the 10-adics), then by "blind faith and unabashed juggling of symbols"<ref>DeSua p.901</ref> one may add the two equations and arrive at …999.999… = 0. This equation does not make sense either as a 10-adic expansion or an ordinary decimal expansion, but it turns out to be meaningful and true if one develops a theory of "double-decimals" with eventually-repeating left ends to represent a familiar system: the real numbers.<ref>DeSua pp.902–903</ref>

==Related questions==

* [[Zeno's paradoxes]], particularly the paradox of the runner, are reminiscent of the apparent paradox that 0.999… and 1 are equal. The runner paradox can be mathematically modelled and then, like 0.999…, resolved using a geometric series. However, it is not clear if this mathematical treatment addresses the underlying metaphysical issues Zeno was exploring.<ref>Wallace p.51, Maor p.17</ref>
* [[Division by zero]] occurs in some popular discussions of 0.999…, and it also stirs up contention. While most authors choose to define 0.999…, almost all modern treatments leave division by zero undefined, as it can be given no meaning in the standard real numbers. However, division by zero is defined in some other systems, such as [[complex analysis]], where the [[extended complex plane]], i.e. the [[Riemann sphere]], has a "[[point at infinity]]". Here, it makes sense to define 1/0 to be infinity;<ref>See, for example, J.B. Conway's treatment of Möbius transformations, pp.47–57</ref> and, in fact, the results are profound and applicable to many problems in engineering and physics. Some prominent mathematicians argued for such a definition long before either number system was developed.<ref>Maor p.54</ref>
* [[Negative zero]] is another redundant feature of many ways of writing numbers. In number systems, such as the real numbers, where "0" denotes the additive identity and is neither positive nor negative, the usual interpretation of "−0" is that it should denote the additive inverse of 0, which forces −0 = 0.<ref>Munkres p.34, Exercise 1(c)</ref> Nonetheless, some scientific applications use separate positive and negative zeroes, as do some of the most common computer number systems (for example integers stored in the [[sign and magnitude]] or [[one's complement]] formats, or floating point numbers as specified by the [[IEEE floating-point standard]]).<ref>{{cite book |author=Kroemer, Herbert; Kittel, Charles |title=Thermal Physics |edition=2e |publisher=W. H. Freeman |year=1980 |id=ISBN 0-7167-1088-9 |pages=462}}</ref><ref>{{cite web |url=http://msdn.microsoft.com/library/en-us/csspec/html/vclrfcsharpspec_4_1_6.asp |title=Floating point types |work=[[Microsoft Developer Network|MSDN]] C# Language Specification |accessdate=2006-08-29}}</ref>

==See also==
{{commons|0.999...}}

* [[Decimal representation]]
* [[Infinity]]
* [[Limit (mathematics)]]
* [[Informal mathematics|Naive mathematics]]
* [[Non-standard analysis]]
* [[Real analysis]]
* [[Series (mathematics)]]

==Notes==
{{reflist|2}}

==References==
<div class="references-small" style="-moz-column-count: 2; column-count: 2;">
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*:This introductory textbook on dynamical systems is aimed at undergraduate and beginning graduate students. (p.ix)
*{{cite book |last=Apostol |first=Tom M. |year=1974 |title=Mathematical analysis |edition=2e |publisher=Addison-Wesley |id=ISBN 0-201-00288-4}}
*:A transition from calculus to advanced analysis, ''Mathematical analysis'' is intended to be "honest, rigorous, up to date, and, at the same time, not too pedantic." (pref.) Apostol's development of the real numbers uses the least upper bound axiom and introduces infinite decimals two pages later. (pp.9–11)
*{{cite book |author=Bartle, R.G. and D.R. Sherbert |year=1982 |title=Introduction to real analysis |publisher=Wiley |id=ISBN 0-471-05944-7}}
*:This text aims to be "an accessible, reasonably paced textbook that deals with the fundamental concepts and techniques of real analysis." Its development of the real numbers relies on the supremum axiom. (pp.vii-viii)
*{{cite book |last=Beals |first=Richard |title=Analysis |year=2004 |publisher=Cambridge UP |id=ISBN 0-521-60047-2}}
*{{cite book |author=[[Elwyn Berlekamp|Berlekamp, E.R.]]; [[John Horton Conway|J.H. Conway]]; and [[Richard K. Guy|R.K. Guy]] |year=1982 |title=[[Winning Ways for your Mathematical Plays]] |publisher=Academic Press |id=ISBN 0-12-091101-9}}
*{{cite conference |last=Berz |first=Martin |title=Automatic differentiation as nonarchimedean analysis |year=1992 |booktitle=Computer Arithmetic and Enclosure Methods |publisher=Elsevier |pages=439–450 |url=http://citeseer.ist.psu.edu/berz92automatic.html}}
*{{cite book |last=Bunch |first=Bryan H. |title=Mathematical fallacies and paradoxes |year=1982 |publisher=Van Nostrand Reinhold |id=ISBN 0-442-24905-5}}
*:This book presents an analysis of paradoxes and fallacies as a tool for exploring its central topic, "the rather tenuous relationship between mathematical reality and physical reality". It assumes first-year high-school algebra; further mathematics is developed in the book, including geometric series in Chapter 2. Although 0.999… is not one of the paradoxes to be fully treated, it is briefly mentioned during a development of Cantor's diagonal method. (pp.ix-xi, 119)
*{{cite book |last=Burrell |first=Brian |title=Merriam-Webster's Guide to Everyday Math: A Home and Business Reference |year=1998 |publisher=Merriam-Webster |id=ISBN 0-87779-621-1}}
*{{cite book |last=Conway |first=John B. |authorlink=John B. Conway |title=Functions of one complex variable I |edition=2e |publisher=Springer-Verlag |origyear=1973 |year=1978 |id=ISBN 0-387-90328-3}}
*:This text assumes "a stiff course in basic calculus" as a prerequisite; its stated principles are to present complex analysis as "An Introduction to Mathematics" and to state the material clearly and precisely. (p.vii)
*{{cite book |last=Davies |first=Charles |year=1846 |title=The University Arithmetic: Embracing the Science of Numbers, and Their Numerous Applications |publisher=A.S. Barnes |url=http://books.google.com/books?vid=LCCN02026287&pg=PA175}}
*{{cite journal |last=DeSua |first=Frank C. |title=A system isomorphic to the reals |format= |journal=The American Mathematical Monthly |volume=67 |number=9 |month=November |year=1960 |pages=900–903 |doi=10.2307/2309468}}
*{{cite journal |author=Dubinsky, Ed, Kirk Weller, Michael McDonald, and Anne Brown |title=Some historical issues and paradoxes regarding the concept of infinity: an APOS analysis: part 2 |journal=Educational Studies in Mathematics |year=2005 |volume=60 |pages=253–266 |doi=10.1007/s10649-005-0473-0}}
*{{cite journal |author=Edwards, Barbara and Michael Ward |year=2004 |month=May |title=Surprises from mathematics education research: Student (mis)use of mathematical definitions |journal=The American Mathematical Monthly |volume=111 |number=5 |pages=411–425 |url=http://www.wou.edu/~wardm/FromMonthlyMay2004.pdf |doi=10.2307/4145268|format=PDF}}
*{{cite book |last=Enderton |first=Herbert B. |year=1977 |title=Elements of set theory |publisher=Elsevier |id=ISBN 0-12-238440-7}}
*:An introductory undergraduate textbook in set theory that "presupposes no specific background". It is written to accommodate a course focusing on axiomatic set theory or on the construction of number systems; the axiomatic material is marked such that it may be de-emphasized. (pp.xi-xii)
*{{cite book |last=Euler |first=Leonhard |authorlink=Leonhard Euler |origyear=1770 |year=1822 |edition=3rd English edition |title=Elements of Algebra |editor=John Hewlett and Francis Horner, English translators. |publisher=Orme Longman |url=http://books.google.com/books?id=X8yv0sj4_1YC&pg=PA170}}
*{{cite journal |last=Fjelstad |first=Paul |title=The repeating integer paradox |format= |journal=The College Mathematics Journal |volume=26 |number=1 |month=January |year=1995 |pages=11–15 |doi=10.2307/2687285}}
*{{cite book |last=Gardiner |first=Anthony |title=Understanding Infinity: The Mathematics of Infinite Processes |origyear=1982 |year=2003 |publisher=Dover |id=ISBN 0-486-42538-X}}
*{{cite book |last=Gowers |first=Timothy|authorlink= William Timothy Gowers|title=Mathematics: A Very Short Introduction |year=2002 |publisher=Oxford UP |id=ISBN 0-19-285361-9}}
*{{cite book |last=Grattan-Guinness |first=Ivor |year=1970 |title=The development of the foundations of mathematical analysis from Euler to Riemann |publisher=MIT Press |id=ISBN 0-262-07034-0}}
*{{cite book | last=Griffiths | first=H.B. | coauthors=P.J. Hilton | title=A Comprehensive Textbook of Classical Mathematics: A Contemporary Interpretation | year=1970 | publisher=Van Nostrand Reinhold | location=London | id=ISBN 0-442-02863-6. {{LCC|QA37.2|G75}}}}
*:This book grew out of a course for [[Birmingham]]-area [[grammar school]] mathematics teachers. The course was intended to convey a university-level perspective on [[mathematics education|school mathematics]], and the book is aimed at students "who have reached roughly the level of completing one year of specialist mathematical study at a university". The real numbers are constructed in Chapter 24, "perhaps the most difficult chapter in the entire book", although the authors ascribe much of the difficulty to their use of [[ideal theory]], which is not reproduced here. (pp.vii, xiv)
*{{cite journal |last=Kempner |first=A.J. |title=Anormal Systems of Numeration |format= |journal=The American Mathematical Monthly |volume=43 |number=10 |month=December |year=1936 |pages=610–617 |doi=10.2307/2300532 }}
*{{cite journal |author=Komornik, Vilmos; and Paola Loreti |title=Unique Developments in Non-Integer Bases |format= |journal=The American Mathematical Monthly |volume=105 |number=7 |year=1998 |pages=636–639 |doi=10.2307/2589246 }}
*{{cite journal |last=Leavitt |first=W.G. |title=A Theorem on Repeating Decimals |format= |journal=The American Mathematical Monthly |volume=74 |number=6 |year=1967 |pages=669–673 |doi=10.2307/2314251 }}
*{{cite journal |last=Leavitt |first=W.G. |title=Repeating Decimals |format= |journal=The College Mathematics Journal |volume=15 |number=4 |month=September |year=1984 |pages=299–308 |doi=10.2307/2686394 }}
*{{cite web | url=http://arxiv.org/abs/math.NT/0605182 |title=Midy's Theorem for Periodic Decimals |last=Lewittes |first=Joseph |work=New York Number Theory Workshop on Combinatorial and Additive Number Theory |year=2006 |publisher=[[arXiv]]}}
*{{cite journal |last=Lightstone |first=A.H. |title=Infinitesimals |format= |journal=The American Mathematical Monthly |year=1972 |volume=79 |number=3 |month=March |pages=242–251 |doi=10.2307/2316619 }}
*{{cite book |last=Mankiewicz |first=Richard |year=2000 |title=The story of mathematics|publisher=Cassell |id=ISBN 0-304-35473-2}}
*:Mankiewicz seeks to represent "the history of mathematics in an accessible style" by combining visual and qualitative aspects of mathematics, mathematicians' writings, and historical sketches. (p.8)
*{{cite book |last=Maor |first=Eli |title=To infinity and beyond: a cultural history of the infinite |year=1987 |publisher=Birkhäuser |id=ISBN 3-7643-3325-1}}
*:A topical rather than chronological review of infinity, this book is "intended for the general reader" but "told from the point of view of a mathematician". On the dilemma of rigor versus readable language, Maor comments, "I hope I have succeeded in properly addressing this problem." (pp.x-xiii)
*{{cite book |last=Mazur |first=Joseph |title=Euclid in the Rainforest: Discovering Universal Truths in Logic and Math |year=2005 |publisher=Pearson: Pi Press |id=ISBN 0-13-147994-6}}
*{{cite book |last=Munkres |first=James R. |title=Topology |year=2000 |origyear=1975 |edition=2e |publisher=Prentice-Hall |id=ISBN 0-13-181629-2}}
*:Intended as an introduction "at the senior or first-year graduate level" with no formal prerequisites: "I do not even assume the reader knows much set theory." (p.xi) Munkres' treatment of the reals is axiomatic; he claims of bare-hands constructions, "This way of approaching the subject takes a good deal of time and effort and is of greater logical than mathematical interest." (p.30)
*{{cite conference |last=Núñez |first=Rafael |title=Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics |year=2006 |booktitle=18 Unconventional Essays on the Nature of Mathematics |publisher=Springer |pages=160–181 |url=http://www.cogsci.ucsd.edu/~nunez/web/publications.html | id=ISBN 978-0-387-25717-4}}
*{{cite book |last=Pedrick |first=George |title=A First Course in Analysis |year=1994 |publisher=Springer |id=ISBN 0-387-94108-8}}
*{{cite journal |last=Petkovšek |first=Marko |title=Ambiguous Numbers are Dense |format= |journal=[[American Mathematical Monthly]] |volume=97 |number=5 |month=May |year=1990 |pages=408–411 |doi=10.2307/2324393 }}
*{{cite conference |author=Pinto, Márcia and David Tall |title=Following students' development in a traditional university analysis course |booktitle=PME25 |pages=v4: 57–64 |year=2001 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001j-pme25-pinto-tall.pdf|format=PDF}}
*{{cite book |author=Protter, M.H. and C.B. Morrey |year=1991 |edition=2e |title=A first course in real analysis |publisher=Springer |id=ISBN 0-387-97437-7}}
*:This book aims to "present a theoretical foundation of analysis that is suitable for students who have completed a standard course in calculus." (p.vii) At the end of Chapter 2, the authors assume as an axiom for the real numbers that bounded, nodecreasing sequences converge, later proving the nested intervals theorem and the least upper bound property. (pp.56–64) Decimal expansions appear in Appendix 3, "Expansions of real numbers in any base". (pp.503–507)
*{{cite book |last=Pugh |first=Charles Chapman |title=Real mathematical analysis |year=2001 |publisher=Springer-Verlag |id=ISBN 0-387-95297-7}}
*:While assuming familiarity with the rational numbers, Pugh introduces [[Dedekind cut]]s as soon as possible, saying of the axiomatic treatment, "This is something of a fraud, considering that the entire structure of analysis is built on the real number system." (p.10) After proving the least upper bound property and some allied facts, cuts are not used in the rest of the book.
*{{cite journal |first=Fred |last=Richman |year=1999 |month=December |title=Is 0.999… = 1? |format= |journal=[[Mathematics Magazine]] |volume=72 |issue=5 |pages=396–400 }} Free HTML preprint: {{cite web |url=http://www.math.fau.edu/Richman/HTML/999.htm |first=Fred|last=Richman|title=Is 0.999… = 1? |date=1999-06-08 |accessdate=2006-08-23}} Note: the journal article contains material and wording not found in the preprint.
*{{cite book |last=Robinson |first=Abraham |authorlink=Abraham Robinson |title=Non-standard analysis |year=1996 |edition=Revised edition |publisher=Princeton University Press|id=ISBN 0-691-04490-2}}
*{{cite book |last=Rosenlicht |first=Maxwell |year=1985 |title=Introduction to Analysis |publisher=Dover |id=ISBN 0-486-65038-3}}
*{{cite book |last=Rudin |first=Walter |authorlink=Walter Rudin |title=Principles of mathematical analysis |edition=3e |year=1976 |origyear=1953 |publisher=McGraw-Hill |id=ISBN 0-07-054235-X}}
*:A textbook for an advanced undergraduate course. "Experience has convinced me that it is pedagogically unsound (though logically correct) to start off with the construction of the real numbers from the rational ones. At the beginning, most students simply fail to appreciate the need for doing this. Accordingly, the real number system is introduced as an ordered field with the least-upper-bound property, and a few interesting applications of this property are quickly made. However, Dedekind's construction is not omitted. It is now in an Appendix to Chapter 1, where it may be studied and enjoyed whenever the time is ripe." (p.ix)
*{{cite journal |last=Shrader-Frechette |first=Maurice |title=Complementary Rational Numbers |format= |journal=Mathematics Magazine |volume=51 |number=2 |month=March |year=1978 |pages=90–98 }}
*{{cite book |author=Smith, Charles and Charles Harrington |year=1895 |title=Arithmetic for Schools |publisher=Macmillan |url=http://books.google.com/books?vid=LCCN02029670&pg=PA115}}
*{{cite book |last=Sohrab |first=Houshang |title=Basic Real Analysis |year=2003 |publisher=Birkhäuser |id=ISBN 0-8176-4211-0}}
*{{cite book |last=Stewart |first=Ian |title=The Foundations of Mathematics |year=1977 |publisher=Oxford UP |id=ISBN 0-19-853165-6}}
*{{cite book |last=Stewart |first=James |title=Calculus: Early transcendentals |edition=4e |year=1999 |publisher=Brooks/Cole |id=ISBN 0-534-36298-2}}
*:This book aims to "assist students in discovering calculus" and "to foster conceptual understanding". (p.v) It omits proofs of the foundations of calculus.
*{{cite journal |author=D.O. Tall and R.L.E. Schwarzenberger |title=Conflicts in the Learning of Real Numbers and Limits |journal=Mathematics Teaching |year=1978 |volume=82 |pages=44–49 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1978c-with-rolph.pdf|format=PDF}}
*{{cite journal |last=Tall |first=David |authorlink=David Tall |title=Conflicts and Catastrophes in the Learning of Mathematics |journal=Mathematical Education for Teaching |year=1976/7 |volume=2 |number=4 |pages=2–18 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1976a-confl-catastrophy.pdf|format=PDF}}
*{{cite journal |last=Tall |first=David |title=Cognitive Development In Advanced Mathematics Using Technology |journal=Mathematics Education Research Journal |year=2000 |volume=12 |number=3 |pages=210–230 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001b-merj-amt.pdf|format=PDF}}
*{{cite book|last=von Mangoldt|first=Dr. Hans|authorlink =Hans Carl Friedrich von Mangoldt| title=Einführung in die höhere Mathematik|edition=1st ed.|year=1911|publisher=Verlag von S. Hirzel| location=Leipzig|language=German|chapter=Reihenzahlen}}
*{{cite book |last=Wallace |first=David Foster|authorlink =David Foster Wallace |title=Everything and more: a compact history of infinity |year=2003 |publisher=Norton |id=ISBN 0-393-00338-8}}
</div>

==External links==
{{Spoken Wikipedia|0.999....ogg|2006-10-19}}
* [http://www.cut-the-knot.org/arithmetic/999999.shtml .999999… = 1?] from [[cut-the-knot]]
* [http://mathforum.org/dr.math/faq/faq.0.9999.html Why does 0.9999… = 1 ?]
* [http://www.newton.dep.anl.gov/askasci/math99/math99167.htm Ask A Scientist: Repeating Decimals]
* [http://mathcentral.uregina.ca/QQ/database/QQ.09.00/joan2.html Proof of the equality based on arithmetic]
* [http://descmath.com/diag/nines.html Repeating Nines]
* [http://qntm.org/pointnine Point nine recurring equals one]
* [http://www.warwick.ac.uk/staff/David.Tall/themes/limits-infinity.html David Tall's research on mathematics cognition]
* [http://www.dpmms.cam.ac.uk/~wtg10/decimals.html What is so wrong with thinking of real numbers as infinite decimals?]
* [http://us.metamath.org/mpegif/0.999....html Theorem 0.999...] on [[Metamath]]

{{featured article}}

[[Category:One]]
[[Category:Mathematics paradoxes]]
[[Category:Real analysis]]
[[Category:Real numbers]]
[[Category:Numeration]]
[[Category:Articles containing proofs]]

{{Link FA|ja}}
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[[fr:Développement décimal de l'unité]]
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Benutzer:Blauerflummi/Testseite Infobox Bahnhof 3

2007-07-15T02:43:35Z

Simetrical: More or less works. Could use some styling to remove the extra margin.

{{Benutzer:Blauerflummi/Infobox Bahnhof 2
| Breite = 270px
| Name = Wien Südbahnhof
| Bild = [[Bild:HamburgHauptbahnhof.jpg|260px|Hamburg Hauptbahnhof aus Richtung Süden]]
| Bildtext = Hamburg Hauptbahnhof aus Richtung Süden
| Eröffnung = 6. Dezember 1906
| Architekt = [[Georg Süßenguth]]
| Architekt_Bezeichnung = Architekten
| Abkürzung = AH
| Kategorie = 1
| Art = Reiterbahnhof
| Stadt = Hamburg
| Bundesland = Hamburg
| Staat = Deutschland
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|Koordinate_Längensekunde=48
|Koordinate_Region=AT-9
|Koordinate_Typ=landmark
| Homepage = [http://www.bahnhof.de/site/bahnhoefe/de/bahnhofssuche__deutschland/bahnhofssuche/bahnhofsdaten__filter,variant=details,recordId=2514.html?c210230=Hamburg Informationen zum Bahnhof]
| Strecken =
* [[Berlin-Hamburger Bahn]] ({{Kursbuchlink|Region=100-199|Nummer=100}})
* [[Hamburg-Altonaer Verbindungsbahn|Verbindungsbahn]] ({{Kursbuchlink|Region=100-199|Nummer=101.1}})
* [[Bahnstrecke Hannover-Hamburg|Hannover-Hamburg]] ({{Kursbuchlink|Region=100-199|Nummer=110}})
* [[Rollbahn (Eisenbahnstrecke)|Rollbahn]] ({{Kursbuchlink|Region=100-199|Nummer=120}})
* [[Niederelbebahn]] ({{Kursbuchlink|Region=100-199|Nummer=121}}
* [[Vogelfluglinie]] ({{Kursbuchlink|Region=100-199|Nummer=140}})
}}
{{Benutzer:Blauerflummi/Infobox Bahnhof 2
| Breite = 270px
| Name = Wien Südbahnhof
| Bild = [[Bild:HamburgHauptbahnhof.jpg|260px|Hamburg Hauptbahnhof aus Richtung Süden]]
| Bildtext = Hamburg Hauptbahnhof aus Richtung Süden
| Eröffnung = 6. Dezember 1906
| Architekt =
* [[Heinrich Reinhardt]]
* [[Georg Süßenguth]]
| Architekt_Bezeichnung = Architekten
| Abkürzung = AH
| Kategorie = 1
| Art = Reiterbahnhof
| Stadt = Hamburg
| Bundesland = Hamburg
| Staat = Deutschland
|Koordinate_Breite=N
|Koordinate_Breitengrad=48
|Koordinate_Breitenminute=11
|Koordinate_Breitensekunde=12
|Koordinate_Länge=O
|Koordinate_Längengrad=16
|Koordinate_Längenminute=22
|Koordinate_Längensekunde=48
|Koordinate_Region=AT-9
|Koordinate_Typ=landmark
| Homepage = [http://www.bahnhof.de/site/bahnhoefe/de/bahnhofssuche__deutschland/bahnhofssuche/bahnhofsdaten__filter,variant=details,recordId=2514.html?c210230=Hamburg Informationen zum Bahnhof]
| Strecken =
* [[Berlin-Hamburger Bahn]] ({{Kursbuchlink|Region=100-199|Nummer=100}})
* [[Hamburg-Altonaer Verbindungsbahn|Verbindungsbahn]] ({{Kursbuchlink|Region=100-199|Nummer=101.1}})
* [[Bahnstrecke Hannover-Hamburg|Hannover-Hamburg]] ({{Kursbuchlink|Region=100-199|Nummer=110}})
* [[Rollbahn (Eisenbahnstrecke)|Rollbahn]] ({{Kursbuchlink|Region=100-199|Nummer=120}})
* [[Niederelbebahn]] ({{Kursbuchlink|Region=100-199|Nummer=121}}
* [[Vogelfluglinie]] ({{Kursbuchlink|Region=100-199|Nummer=140}})
}}
Testseite

Benutzer:Blauerflummi/Infobox Bahnhof 2

2007-07-15T02:42:20Z

Simetrical:

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|-
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{{!}} {{#switch: {{{Kategorie|}}}
| 1 = Fernverkehrsknoten
| 2 = Fernverkehrssystemhalt
| 3 = Regionalknoten/ Fernverkehrshalt
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! Bahnsteiggleise
{{!}}{{{Bahnsteiggleise|}}}
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|- style="border-top: solid 1px #ccd2d9; vertical-align: top"
! style="padding: 0.4em 0.4em 0.4em 0em;"|[[Geographische Koordinaten|Koordinaten]]
| colspan="2" style="padding: 0.4em 0em 0.4em 0em;" |{{#if:{{{Koordinate_Breite|}}}
|<div style="width: 7.5em; margin: 0; padding: 0;"><noinclude></noinclude>{{Koordinate Text Artikel
|{{{Koordinate_Breitengrad|00}}}_{{{Koordinate_Breitenminute|00}}}_{{{Koordinate_Breitensekunde|00}}}_{{{Koordinate_Breite|N}}}_{{{Koordinate_Längengrad|000}}}_{{{Koordinate_Längenminute|00}}}_{{{Koordinate_Längensekunde|00}}}_{{#ifeq:{{{Koordinate_Länge|O}}}|O|E|{{{Koordinate_Länge|}}}}}_type:landmark_region:{{{Koordinate_Region|DE}}}|<noinclude></noinclude>{{#expr:{{{Koordinate_Breitengrad|0}}}round 0}}° {{#ifexpr: {{{Koordinate_Breitenminute|0}}} < 9.5|0}}{{#expr:{{{Koordinate_Breitenminute|0}}} round 0}}′ {{#ifexpr: {{#expr:{{{Koordinate_Breitensekunde|0}}} round 0}} < 9.5 |0}}{{#expr: {{{Koordinate_Breitensekunde|0}}} round 0}}″ {{{Koordinate_Breite|N}}} {{#expr:{{{Koordinate_Längengrad|0}}} round 0}}° {{#ifexpr: {{{Koordinate_Längenminute|0}}} < 9.5|0}}{{#expr:{{{Koordinate_Längenminute|0}}} round 0}}′ {{#ifexpr:
{{#expr:{{{Koordinate_Längensekunde|0}}} round 0}} < 9.5 |0}}{{#expr:{{{Koordinate_Längensekunde|0}}} round 0}}″ {{{Koordinate_Länge|O}}} }}
}}</div>
|- valign="top"
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | {{#if: {{{Strecken|}}} | Eisenbahnstrecken }}
|-
| colspan="2" | {{#if: {{{Strecken|}}} | {{{Strecken|}}} }}
|-
!colspan="2" style="text-align: center;" class="hintergrundfarbe6" |{{#switch: {{{Bundesland}}}
| Baden-Württemberg = [[Bild:Coat of arms of Baden-Württemberg (lesser).svg|20px]] [[Liste der Bahnhöfe in Baden-Württemberg]]
| Bayern = [[ Bild:Landessymbol Bayern.PNG|20px]] [[Liste der Bahnhöfe in Bayern]]
| Berlin = [[Bild:Country symbol of Berlin color.svg|20px]] [[Liste der Bahnhöfe im Raum Berlin]]
| Brandenburg = [[Bild:Brandenburg Wappen.svg|20px]] [[Liste der Bahnhöfe in Brandenburg]]
| Bremen = [[Bild:Bremen Wappen frei.svg|20px]] [[Bremen (Land)#Liste der Bahnhöfe in Bremen|Liste der Bahnhöfe in Bremen]]
| Hamburg = [[Bild:Coat of arms of Hamburg.svg|20px]] [[Liste Hamburger Bahnhöfe]]
| Hessen = [[Bild:Coat of arms of Hesse.svg|20px]] [[Liste der Bahnhöfe in Hessen]] bzw. [[Liste der SPNV-Stationen in Hessen]]
| Mecklenburg-Vorpommern = [[Bild:Coat of arms of Mecklenburg-Western Pomerania (small).svg|20px]] [[Eisenbahnlinien in Mecklenburg-Vorpommern#Bahnhöfe|Liste der Bahnhöfe in Mecklenburg-Vorpommern]]
| Niedersachsen = [[Bild:Coat of arms of Lower Saxony.svg|20px]] [[Liste der Bahnhöfe in Niedersachsen]]
| Nordrhein-Westfalen = [[Bild:Coat of arms of North Rhine-Westfalia.svg|20px]] [[Liste der Bahnhöfe in Nordrhein-Westfalen]]
| Rheinland-Pfalz =[[Bild:Coat of arms of Rhineland-Palatinate.svg|20px]] [[Liste der Bahnhöfe in Rheinland-Pfalz]]
| Saarland = [[Bild:Coa de-saarland 300px.png|20px]] [[Saarland#Bahnhofskategorien|Liste der Bahnhöfe im Saarland]]
| Sachsen-Anhalt = [[Bild:Wappen Sachsen-Anhalt.svg|20px]] [[Liste der Bahnhöfe in Sachsen-Anhalt]]
| Sachsen =[[Bild:Coat of arms of Saxony.svg|20px]] [[Liste der Bahnhöfe in Sachsen]]
| Schleswig-Holstein =[[Bild:Coat of arms of Schleswig-Holstein.svg|20px]] [[Liste der Bahnhöfe in Schleswig-Holstein]]
| Thüringen = [[Bild:Coat of arms of Thuringia.svg|20px]] [[Liste der Bahnhöfe in Thüringen]]
}}
|-
!colspan="2" style="text-align: center;" class="hintergrundfarbe6" |{{#switch: {{{Staat}}}
| Niederlande = [[Bild:Nl-arms.gif|20px]] [[Liste der Bahnhöfe in den Niederlanden]]
}}
|}
Test

Benutzer:Simetrical

2007-07-15T02:41:49Z

Simetrical:

[[:en:User:Simetrical]]. I have an account here in case people report bugs or whatever and give test cases that are here.

Benutzer:Simetrical

2007-07-15T02:41:40Z

Simetrical: AZ: Die Seite wurde neu angelegt.

[[:en:User:Simetrical]]. I have an accoun there in case people report bugs or whatever and give test cases that are here.

Benutzer:Blauerflummi/Testseite Infobox Bahnhof 3

2007-07-15T02:40:53Z

Simetrical: Fidget

Benutzer:Blauerflummi/Infobox Bahnhof 2

2007-07-15T02:16:51Z

Simetrical: Fix bug

{| class="toccolours" style="float: right; margin: 0 0 1em 1em; width:{{{Breite|300px}}}; font-size: 90%; clear:right; vertical-align: top; text-align: left; empty-cells:collapse;" cellspacing="5"
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | {{#if: {{{Name|}}} | {{{Name|}}} | {{PAGENAME}} }}
|-
<noinclude></noinclude>
|- style="border-top: solid 1px #ccd2d9;"
| colspan="2" style="padding: 0.2em 0em 0.2em 0em; text-align: center;"| {{#if: {{{Bild|}}}
| <div style="margin: 0.2em 0em 0.2em 0em;padding: 0;">{{{Bild}}}</div>
{{!-}}
{{#if: {{{Bildtext|}}}|
{{!}} colspan="2" {{!}} <center>{{{Bildtext}}}</center>
{{!-}}
}}
| {{#if: {{{Koordinate_Region|}}}
| {{#ifeq: {{Positionskarte ISO 3166-2|{{{Koordinate_Region|}}}|label=|lat_dir={{{Koordinate_Breite|N}}}|lat_deg={{{Koordinate_Breitengrad|50}}}|lat_min={{{Koordinate_Breitenminute|0}}}|lat_sec={{{Koordinate_Breitensekunde|0}}}|lon_dir={{{Koordinate_Länge|}}}|lon_deg={{{Koordinate_Längengrad|08}}}|lon_min={{{Koordinate_Längenminute|0}}}|lon_sec={{{Koordinate_Längensekunde|0}}}|caption=|border=none|float=center|width=250|warning=Koordinatenfehler}}||
|<div style="margin: 0.2em 0em 0.2em 0em;padding: 0;">{{Positionskarte ISO 3166-2|{{{Koordinate_Region|}}}|label=|lat_dir={{{Koordinate_Breite|N}}}|lat_deg={{{Koordinate_Breitengrad|50}}}|lat_min={{{Koordinate_Breitenminute|0}}}|lat_sec={{{Koordinate_Breitensekunde|0}}}|lon_dir={{{Koordinate_Länge|}}}|lon_deg={{{Koordinate_Längengrad|08}}}|lon_min={{{Koordinate_Längenminute|0}}}|lon_sec={{{Koordinate_Längensekunde|0}}}|caption=|border=none|float=center|width=250|warning=Koordinatenfehler}}</div>
}}
}}
}}
|-
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | Bahnhofsdaten
|-
{{#if: {{{Kategorie|}}} |
! [[Bahnhofskategorie|Kategorie]]
{{!}} {{#switch: {{{Kategorie|}}}
| 1 = Fernverkehrsknoten
| 2 = Fernverkehrssystemhalt
| 3 = Regionalknoten/ Fernverkehrshalt
| 4 = Nahverkehrssystemhalt/ Nahverkehrsknoten
| 5 = Nahverkehrssystemhalt
| 6 = Nahverkehrshalt
| #default = {{{Bahnhofskategorie}}}
}}
}}
|- valign="top"
{{#if: {{{Art|}}} |
! [[Bahnhof#Bahnhofsarten|Art]]
{{!}} [[{{{Art|}}}]]
}}
|- valign="top"
{{#if: {{{Bahnsteiggleise|}}} |
! Bahnsteiggleise
{{!}}{{{Bahnsteiggleise|}}}
}}
|- valign="top"
{{#if: {{{Reisende|}}} |
! Reisende
{{!}} {{{Reisende|}}}
}}
|- valign="top"
{{#if: {{{Zugfahrten|}}} |
! tägl. Zugfahrten
{{!}} {{{Zugfahrten|}}}
}}
|- valign="top"
{{#if: {{{Abkürzung|}}} |
! [[Bahnamtliches Betriebsstellenverzeichnis|Abkürzung]]
{{!}} {{{Abkürzung|}}}
}}
|- valign="top"
{{#if: {{{Homepage|}}} |
! Webadresse
{{!}} {{{Homepage|}}}
}}
|-
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | Architektonische Daten
|- valign="top"
{{#if: {{{Eröffnung|}}} |
! Eröffnung
{{!}} {{{Eröffnung|}}}
}}
|- valign="top"
{{#if: {{{Stilllegung|}}} |
! Stilllegung
{{!}} {{{Stilllegung|}}}
}}
|- valign="top"
{{#if: {{{Architekt|}}} |
! {{#if: {{{Architekt_Bezeichnung|}}}|
{{{Architekt_Bezeichnung|}}}|Architekt
}}
{{!}} {{{Architekt|}}}
}}
|- valign="top"
{{#if: {{{Baustil|}}} |
! [[Baustil]]
{{!}} {{{Baustil|}}}
}}
|- valign="top"
! Stadt
| [[{{{Stadt|}}}]]

|- valign="top"
{{#if: {{{Bundesland|}}} |
! {{#if: {{{Bundesland_Bezeichnung|}}}|
{{{Bundesland_Bezeichnung|}}}|Bundesland
}}
{{!}} {{#switch: {{{Bundesland|}}}
| Baden-Württemberg = {{DEU-BW}}
| Bayern = {{DEU-BY}}
| Berlin = {{DEU-BE}}
| Brandenburg = {{DEU-BR}}
| Bremen = {{DEU-HB}}
| Hamburg = {{DEU-HH}}
| Hessen = {{DEU-HE}}
| Mecklenburg-Vorpommern = {{DEU-MV}}
| Niedersachsen = {{DEU-NI}}
| Nordrhein-Westfalen = {{DEU-NW}}
| Rheinland-Pfalz = {{DEU-RP}}
| Saarland = {{DEU-SL}}
| Sachsen-Anhalt = {{DEU-ST}}
| Sachsen = {{DEU-SN}}
| Schleswig-Holstein = {{DEU-SH}}
| Thüringen = {{DEU-TH}}
| #default = {{{Bundesland}}}
}}
}}
|- valign="top"
! Staat
| {{#switch: {{{Staat|}}}
| Afghanistan = {{AFG}}
| Ägypten = {{EGY}}
| Åland = {{ALA}}
| Albanien = {{ALB}}
| Algerien = {{DZA}}
| Andorra = {{AND}}
| Angola = {{AGO}}
| Anguilla = {{AIA}}
| Argentinien = {{ARG}}
| Armenien = {{ARM}}
| Aruba = {{ABW}}
| Äthiopien = {{ETH}}
| Australien = {{AUS}}
| Bahamas = {{BHS}}
| Bahrain = {{BHR}}
| Bangladesch = {{BGD}}
| Barbados = {{BRB}}
| Weißrussland = {{BLR}}
| Belgien = {{BEL}}
| Belize = {{BLZ}}
| Benin = {{BEN}}
| Bermuda = {{BMU}}
| Bhutan = {{BTN}}
| Bolivien = {{BOL}}
| Botswana = {{BWA}}
| Bouvetinsel = {{BVT}}
| Brasilien = {{BRA}}
| Bulgarien = {{BGR}}
| Burkina Faso = {{BFA}}
| Burma = {{MMR}}
| Burundi = {{BDI}}
| Chile = {{CHL}}
| China = {{CHN}}
| Cookinseln = {{COK}}
| Costa Rica = {{CRI}}
| Dänemark = {{DNK}}
| Deutschland = {{DEU}}
| Dominica = {{DMA}}
| Dominikanische Republik= {{DOM}}
| Dschibuti = {{DJI}}
| Ecuador = {{ECU}}
| El Salvador = {{SLV}}
| Elfenbeinküste= {{CIV}}
| England = {{ENG}}
| Eritrea = {{ERI}}
| Estland = {{EST}}
| Falklandinseln= {{FLK}}
| Färöer = {{FRO}}
| Fidschi = {{FJI}}
| Finnland = {{FIN}}
| Frankreich = {{FRA}}
| Gabun = {{GAB}}
| Gambia = {{GMB}}
| Georgien = {{GEO}}
| Ghana = {{GHA}}
| Gibraltar = {{GIB}}
| Grenada = {{GRD}}
| Griechenland = {{GRC}}
| Grönland = {{GRL}}
| Guadeloupe = {{GLP}}
| Guam = {{GUM}}
| Guatemala = {{GTM}}
| Guinea = {{GIN}}
| Guinea-Bissau = {{GNB}}
| Guyana = {{GUY}}
| Haiti = {{HTI}}
| Honduras = {{HND}}
| Hongkong = {{HKG}}
| Indien = {{IND}}
| Indonesien = {{IDN}}
| Insel Man = {{IMN}}
| Irak = {{IRQ}}
| Iran = {{IRN}}
| Irland = {{IRL}}
| Island = {{ISL}}
| Israel = {{ISR}}
| Italien = {{ITA}}
| Jamaika = {{JAM}}
| Japan = {{JPN}}
| Jemen = {{YEM}}
| Jordanien = {{JOR}}
| Kaimaninseln = {{CYM}}
| Kambodscha = {{KHM}}
| Kamerun = {{CMR}}
| Kanada = {{CAN}}
| Kap Verde = {{CPV}}
| Kasachstan = {{KAZ}}
| Katar = {{QAT}}
| Kenia = {{KEN}}
| Kirgisistan = {{KGZ}}
| Kiribati = {{KIR}}
| Kolumbien = {{COL}}
| Komoren = {{COM}}
| Kroatien = {{HRV}}
| Kuba = {{CUB}}
| Kuwait = {{KWT}}
| Laos = {{LAO}}
| Lesotho = {{LSO}}
| Lettland = {{LVA}}
| Libanon = {{LBN}}
| Liberia = {{LBR}}
| Libyen = {{LBY}}
| Liechtenstein = {{LIE}}
| Litauen = {{LTU}}
| Luxemburg = {{LUX}}
| Macao = {{MAC}}
| Madagaskar = {{MDG}}
| Malawi = {{MWI}}
| Malaysia = {{MYS}}
| Malediven = {{MDV}}
| Mali = {{MLI}}
| Malta = {{MLT}}
| Marokko = {{MAR}}
| Marshallinseln= {{MHL}}
| Martinique = {{MTQ}}
| Mauretanien = {{MRT}}
| Mauritius = {{MUS}}
| Mayotte = {{MYT}}
| Mazedonien = {{MKD}}
| Mexiko = {{MEX}}
| Mikronesien = {{FSM}}
| Moldawien = {{MDA}}
| Monaco = {{MCO}}
| Mongolei = {{MNG}}
| Montenegro = {{MNE}}
| Montserrat = {{MSR}}
| Mosambik = {{MOZ}}
| Namibia = {{NAM}}
| Nauru = {{NRU}}
| Nepal = {{NPL}}
| Neukaledonien = {{NCL}}
| Neuseeland = {{NZL}}
| Nicaragua = {{NIC}}
| Niederlande = {{NLD}}
| Niederländische Antillen= {{ANT}}
| Niger = {{NER}}
| Nigeria = {{NGA}}
| Nordkorea = {{PRK}}
| Norwegen = {{NOR}}
| Oman = {{OMN}}
| Österreich = {{AUT}}
| Osttimor = {{TLS}}
| Pakistan = {{PAK}}
| Palau = {{PLW}}
| Panama = {{PAN}}
| Papua-Neuguinea= {{PNG}}
| Paraguay = {{PRY}}
| Peru = {{PER}}
| Philippinen = {{PHL}}
| Pitcairninseln= {{PCN}}
| Polen = {{POL}}
| Portugal = {{PRT}}
| Puerto Rico = {{PRI}}
| Republik Kongo= {{COG}}
| Réunion = {{REU}}
| Ruanda = {{RWA}}
| Rumänien = {{ROU}}
| Russland = {{RUS}}
| Salomonen = {{SLB}}
| Sambia = {{ZMB}}
| Samoa = {{WSM}}
| San Marino = {{SMR}}
| Saudi-Arabien = {{SAU}}
| Schweden = {{SWE}}
| Schweiz = {{CHE}}
| Senegal = {{SEN}}
| Serbien = {{SRB}}
| Seychellen = {{SYC}}
| Sierra Leone = {{SLE}}
| Simbabwe = {{ZWE}}
| Singapur = {{SGP}}
| Slowakei = {{SVK}}
| Slowenien = {{SVN}}
| Somalia = {{SOM}}
| Spanien = {{ESP}}
| Sri Lanka = {{LKA}}
| Südafrika = {{ZAF}}
| Südkorea = {{KOR}}
| Sudan = {{SDN}}
| Suriname = {{SUR}}
| Swasiland = {{SWZ}}
| Syrien = {{SYR}}
| Tadschikistan = {{TJK}}
| Tansania = {{TZA}}
| Thailand = {{THA}}
| Timor-Leste = {{TLS}}
| Togo = {{TGO}}
| Tokelau = {{TKL}}
| Tonga = {{TON}}
| Trinidad und Tobago= {{TTO}}
| Tschad = {{TCD}}
| Tschechische Republik= {{CZE}}
| Tunesien = {{TUN}}
| Türkei = {{TUR}}
| Turkmenistan = {{TKM}}
| Tuvalu = {{TUV}}
| Uganda = {{UGA}}
| Ukraine = {{UKR}}
| Ungarn = {{HUN}}
| Uruguay = {{URY}}
| Usbekistan = {{UZB}}
| Vanuatu = {{VUT}}
| Venezuela = {{VEN}}
| Vereinigte Arabische Emirate= {{ARE}}
| Vereinigte Staaten= {{USA}}
| Vereinigtes Königreich= {{GBR}}
| Vietnam = {{VNM}}
| Westsahara = {{ESH}}
| Zypern = {{CYP}}
| #default = {{{Staat}}}
}}
|- style="border-top: solid 1px #ccd2d9; vertical-align: top"
! style="padding: 0.4em 0.4em 0.4em 0em;"|[[Geographische Koordinaten|Koordinaten]]
| colspan="2" style="padding: 0.4em 0em 0.4em 0em;" |{{#if:{{{Koordinate_Breite|}}}
|<div style="width: 7.5em; margin: 0; padding: 0;"><noinclude></noinclude>{{Koordinate Text Artikel
|{{{Koordinate_Breitengrad|00}}}_{{{Koordinate_Breitenminute|00}}}_{{{Koordinate_Breitensekunde|00}}}_{{{Koordinate_Breite|N}}}_{{{Koordinate_Längengrad|000}}}_{{{Koordinate_Längenminute|00}}}_{{{Koordinate_Längensekunde|00}}}_{{#ifeq:{{{Koordinate_Länge|O}}}|O|E|{{{Koordinate_Länge|}}}}}_type:landmark_region:{{{Koordinate_Region|DE}}}|<noinclude></noinclude>{{#expr:{{{Koordinate_Breitengrad|0}}}round 0}}° {{#ifexpr: {{{Koordinate_Breitenminute|0}}} < 9.5|0}}{{#expr:{{{Koordinate_Breitenminute|0}}} round 0}}′ {{#ifexpr: {{#expr:{{{Koordinate_Breitensekunde|0}}} round 0}} < 9.5 |0}}{{#expr: {{{Koordinate_Breitensekunde|0}}} round 0}}″ {{{Koordinate_Breite|N}}} {{#expr:{{{Koordinate_Längengrad|0}}} round 0}}° {{#ifexpr: {{{Koordinate_Längenminute|0}}} < 9.5|0}}{{#expr:{{{Koordinate_Längenminute|0}}} round 0}}′ {{#ifexpr:
{{#expr:{{{Koordinate_Längensekunde|0}}} round 0}} < 9.5 |0}}{{#expr:{{{Koordinate_Längensekunde|0}}} round 0}}″ {{{Koordinate_Länge|O}}} }}
}}</div>
|- valign="top"
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | {{#if: {{{Strecken|}}} | Eisenbahnstrecken }}
|-
| colspan="2" | {{#if: {{{Strecken|}}} | {{{Strecken|}}} }}
|-
!colspan="2" style="text-align: center;" class="hintergrundfarbe6" |{{#switch: {{{Bundesland}}}
| Baden-Württemberg = [[Bild:Coat of arms of Baden-Württemberg (lesser).svg|20px]] [[Liste der Bahnhöfe in Baden-Württemberg]]
| Bayern = [[ Bild:Landessymbol Bayern.PNG|20px]] [[Liste der Bahnhöfe in Bayern]]
| Berlin = [[Bild:Country symbol of Berlin color.svg|20px]] [[Liste der Bahnhöfe im Raum Berlin]]
| Brandenburg = [[Bild:Brandenburg Wappen.svg|20px]] [[Liste der Bahnhöfe in Brandenburg]]
| Bremen = [[Bild:Bremen Wappen frei.svg|20px]] [[Bremen (Land)#Liste der Bahnhöfe in Bremen|Liste der Bahnhöfe in Bremen]]
| Hamburg = [[Bild:Coat of arms of Hamburg.svg|20px]] [[Liste Hamburger Bahnhöfe]]
| Hessen = [[Bild:Coat of arms of Hesse.svg|20px]] [[Liste der Bahnhöfe in Hessen]] bzw. [[Liste der SPNV-Stationen in Hessen]]
| Mecklenburg-Vorpommern = [[Bild:Coat of arms of Mecklenburg-Western Pomerania (small).svg|20px]] [[Eisenbahnlinien in Mecklenburg-Vorpommern#Bahnhöfe|Liste der Bahnhöfe in Mecklenburg-Vorpommern]]
| Niedersachsen = [[Bild:Coat of arms of Lower Saxony.svg|20px]] [[Liste der Bahnhöfe in Niedersachsen]]
| Nordrhein-Westfalen = [[Bild:Coat of arms of North Rhine-Westfalia.svg|20px]] [[Liste der Bahnhöfe in Nordrhein-Westfalen]]
| Rheinland-Pfalz =[[Bild:Coat of arms of Rhineland-Palatinate.svg|20px]] [[Liste der Bahnhöfe in Rheinland-Pfalz]]
| Saarland = [[Bild:Coa de-saarland 300px.png|20px]] [[Saarland#Bahnhofskategorien|Liste der Bahnhöfe im Saarland]]
| Sachsen-Anhalt = [[Bild:Wappen Sachsen-Anhalt.svg|20px]] [[Liste der Bahnhöfe in Sachsen-Anhalt]]
| Sachsen =[[Bild:Coat of arms of Saxony.svg|20px]] [[Liste der Bahnhöfe in Sachsen]]
| Schleswig-Holstein =[[Bild:Coat of arms of Schleswig-Holstein.svg|20px]] [[Liste der Bahnhöfe in Schleswig-Holstein]]
| Thüringen = [[Bild:Coat of arms of Thuringia.svg|20px]] [[Liste der Bahnhöfe in Thüringen]]
}}
|-
!colspan="2" style="text-align: center;" class="hintergrundfarbe6" |{{#switch: {{{Staat}}}
| Niederlande = [[Bild:Nl-arms.gif|20px]] [[Liste der Bahnhöfe in den Niederlanden]]
}}
|}
Test

Benutzer:Blauerflummi/Testseite Infobox Bahnhof 3

2007-07-15T02:15:59Z

Simetrical: Test

Benutzer:Blauerflummi/Infobox Bahnhof 2

2007-07-15T02:15:33Z

Simetrical: Test

{| class="toccolours" style="float: right; margin: 0 0 1em 1em; width:{{{Breite|300px}}}; font-size: 90%; clear:right; vertical-align: top; text-align: left; empty-cells:collapse;" cellspacing="5"
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | {{#if: {{{Name|}}} | {{{Name|}}} | {{PAGENAME}} }}
|-
<noinclude></noinclude>
|- style="border-top: solid 1px #ccd2d9;"
| colspan="2" style="padding: 0.2em 0em 0.2em 0em; text-align: center;"| {{#if: {{{Bild|}}}
| <div style="margin: 0.2em 0em 0.2em 0em;padding: 0;">{{{Bild}}}</div>
{{!-}}
{{#if: {{{Bildtext|}}}|
{{!}} colspan="2" {{!}} <center>{{{Bildtext}}}</center>
{{!-}}
}}
| {{#if: {{{Koordinate_Region|}}}
| {{#ifeq: {{Positionskarte ISO 3166-2|{{{Koordinate_Region|}}}|label=|lat_dir={{{Koordinate_Breite|N}}}|lat_deg={{{Koordinate_Breitengrad|50}}}|lat_min={{{Koordinate_Breitenminute|0}}}|lat_sec={{{Koordinate_Breitensekunde|0}}}|lon_dir={{{Koordinate_Länge|}}}|lon_deg={{{Koordinate_Längengrad|08}}}|lon_min={{{Koordinate_Längenminute|0}}}|lon_sec={{{Koordinate_Längensekunde|0}}}|caption=|border=none|float=center|width=250|warning=Koordinatenfehler}}||
|<div style="margin: 0.2em 0em 0.2em 0em;padding: 0;">{{Positionskarte ISO 3166-2|{{{Koordinate_Region|}}}|label=|lat_dir={{{Koordinate_Breite|N}}}|lat_deg={{{Koordinate_Breitengrad|50}}}|lat_min={{{Koordinate_Breitenminute|0}}}|lat_sec={{{Koordinate_Breitensekunde|0}}}|lon_dir={{{Koordinate_Länge|}}}|lon_deg={{{Koordinate_Längengrad|08}}}|lon_min={{{Koordinate_Längenminute|0}}}|lon_sec={{{Koordinate_Längensekunde|0}}}|caption=|border=none|float=center|width=250|warning=Koordinatenfehler}}</div>
}}
}}
}}
|-
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | Bahnhofsdaten
|-
{{#if: {{{Kategorie|}}} |
! [[Bahnhofskategorie|Kategorie]]
{{!}} {{#switch: {{{Kategorie|}}}
| 1 = Fernverkehrsknoten
| 2 = Fernverkehrssystemhalt
| 3 = Regionalknoten/ Fernverkehrshalt
| 4 = Nahverkehrssystemhalt/ Nahverkehrsknoten
| 5 = Nahverkehrssystemhalt
| 6 = Nahverkehrshalt
| #default = {{{Bahnhofskategorie}}}
}}
}}
|- valign="top"
{{#if: {{{Art|}}} |
! [[Bahnhof#Bahnhofsarten|Art]]
{{!}} [[{{{Art|}}}]]
}}
|- valign="top"
{{#if: {{{Bahnsteiggleise|}}} |
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{{!}}{{{Bahnsteiggleise|}}}
}}
|- valign="top"
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! Reisende
{{!}} {{{Reisende|}}}
}}
|- valign="top"
{{#if: {{{Zugfahrten|}}} |
! tägl. Zugfahrten
{{!}} {{{Zugfahrten|}}}
}}
|- valign="top"
{{#if: {{{Abkürzung|}}} |
! [[Bahnamtliches Betriebsstellenverzeichnis|Abkürzung]]
{{!}} {{{Abkürzung|}}}
}}
|- valign="top"
{{#if: {{{Homepage|}}} |
! Webadresse
{{!}} {{{Homepage|}}}
}}
|-
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | Architektonische Daten
|- valign="top"
{{#if: {{{Eröffnung|}}} |
! Eröffnung
{{!}} {{{Eröffnung|}}}
}}
|- valign="top"
{{#if: {{{Stilllegung|}}} |
! Stilllegung
{{!}} {{{Stilllegung|}}}
}}
|- valign="top"
{{#if: {{{Architekt|}}} |
! {{#if: {{{Architekt_Bezeichnung|}}}|
{{{Architekt_Bezeichnung|}}}|Architekt
}} {{!}} {{{Architekt|}}}
}}
|- valign="top"
{{#if: {{{Baustil|}}} |
! [[Baustil]]
{{!}} {{{Baustil|}}}
}}
|- valign="top"
! Stadt
| [[{{{Stadt|}}}]]

|- valign="top"
{{#if: {{{Bundesland|}}} |
! {{#if: {{{Bundesland_Bezeichnung|}}}|
{{{Bundesland_Bezeichnung|}}}|Bundesland
}}
{{!}} {{#switch: {{{Bundesland|}}}
| Baden-Württemberg = {{DEU-BW}}
| Bayern = {{DEU-BY}}
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| Hessen = {{DEU-HE}}
| Mecklenburg-Vorpommern = {{DEU-MV}}
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| Schleswig-Holstein = {{DEU-SH}}
| Thüringen = {{DEU-TH}}
| #default = {{{Bundesland}}}
}}
}}
|- valign="top"
! Staat
| {{#switch: {{{Staat|}}}
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| Åland = {{ALA}}
| Albanien = {{ALB}}
| Algerien = {{DZA}}
| Andorra = {{AND}}
| Angola = {{AGO}}
| Anguilla = {{AIA}}
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| Armenien = {{ARM}}
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| China = {{CHN}}
| Cookinseln = {{COK}}
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| Dänemark = {{DNK}}
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| Insel Man = {{IMN}}
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| Iran = {{IRN}}
| Irland = {{IRL}}
| Island = {{ISL}}
| Israel = {{ISR}}
| Italien = {{ITA}}
| Jamaika = {{JAM}}
| Japan = {{JPN}}
| Jemen = {{YEM}}
| Jordanien = {{JOR}}
| Kaimaninseln = {{CYM}}
| Kambodscha = {{KHM}}
| Kamerun = {{CMR}}
| Kanada = {{CAN}}
| Kap Verde = {{CPV}}
| Kasachstan = {{KAZ}}
| Katar = {{QAT}}
| Kenia = {{KEN}}
| Kirgisistan = {{KGZ}}
| Kiribati = {{KIR}}
| Kolumbien = {{COL}}
| Komoren = {{COM}}
| Kroatien = {{HRV}}
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| Kuwait = {{KWT}}
| Laos = {{LAO}}
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| Lettland = {{LVA}}
| Libanon = {{LBN}}
| Liberia = {{LBR}}
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| Luxemburg = {{LUX}}
| Macao = {{MAC}}
| Madagaskar = {{MDG}}
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| Malaysia = {{MYS}}
| Malediven = {{MDV}}
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| Malta = {{MLT}}
| Marokko = {{MAR}}
| Marshallinseln= {{MHL}}
| Martinique = {{MTQ}}
| Mauretanien = {{MRT}}
| Mauritius = {{MUS}}
| Mayotte = {{MYT}}
| Mazedonien = {{MKD}}
| Mexiko = {{MEX}}
| Mikronesien = {{FSM}}
| Moldawien = {{MDA}}
| Monaco = {{MCO}}
| Mongolei = {{MNG}}
| Montenegro = {{MNE}}
| Montserrat = {{MSR}}
| Mosambik = {{MOZ}}
| Namibia = {{NAM}}
| Nauru = {{NRU}}
| Nepal = {{NPL}}
| Neukaledonien = {{NCL}}
| Neuseeland = {{NZL}}
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| Niederländische Antillen= {{ANT}}
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| Osttimor = {{TLS}}
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| Palau = {{PLW}}
| Panama = {{PAN}}
| Papua-Neuguinea= {{PNG}}
| Paraguay = {{PRY}}
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| Philippinen = {{PHL}}
| Pitcairninseln= {{PCN}}
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| San Marino = {{SMR}}
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| Swasiland = {{SWZ}}
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| Tansania = {{TZA}}
| Thailand = {{THA}}
| Timor-Leste = {{TLS}}
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| Tokelau = {{TKL}}
| Tonga = {{TON}}
| Trinidad und Tobago= {{TTO}}
| Tschad = {{TCD}}
| Tschechische Republik= {{CZE}}
| Tunesien = {{TUN}}
| Türkei = {{TUR}}
| Turkmenistan = {{TKM}}
| Tuvalu = {{TUV}}
| Uganda = {{UGA}}
| Ukraine = {{UKR}}
| Ungarn = {{HUN}}
| Uruguay = {{URY}}
| Usbekistan = {{UZB}}
| Vanuatu = {{VUT}}
| Venezuela = {{VEN}}
| Vereinigte Arabische Emirate= {{ARE}}
| Vereinigte Staaten= {{USA}}
| Vereinigtes Königreich= {{GBR}}
| Vietnam = {{VNM}}
| Westsahara = {{ESH}}
| Zypern = {{CYP}}
| #default = {{{Staat}}}
}}
|- style="border-top: solid 1px #ccd2d9; vertical-align: top"
! style="padding: 0.4em 0.4em 0.4em 0em;"|[[Geographische Koordinaten|Koordinaten]]
| colspan="2" style="padding: 0.4em 0em 0.4em 0em;" |{{#if:{{{Koordinate_Breite|}}}
|<div style="width: 7.5em; margin: 0; padding: 0;"><noinclude></noinclude>{{Koordinate Text Artikel
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{{#expr:{{{Koordinate_Längensekunde|0}}} round 0}} < 9.5 |0}}{{#expr:{{{Koordinate_Längensekunde|0}}} round 0}}″ {{{Koordinate_Länge|O}}} }}
}}</div>
|- valign="top"
! colspan="2" style="text-align: center;" class="hintergrundfarbe6" | {{#if: {{{Strecken|}}} | Eisenbahnstrecken }}
|-
| colspan="2" | {{#if: {{{Strecken|}}} | {{{Strecken|}}} }}
|-
!colspan="2" style="text-align: center;" class="hintergrundfarbe6" |{{#switch: {{{Bundesland}}}
| Baden-Württemberg = [[Bild:Coat of arms of Baden-Württemberg (lesser).svg|20px]] [[Liste der Bahnhöfe in Baden-Württemberg]]
| Bayern = [[ Bild:Landessymbol Bayern.PNG|20px]] [[Liste der Bahnhöfe in Bayern]]
| Berlin = [[Bild:Country symbol of Berlin color.svg|20px]] [[Liste der Bahnhöfe im Raum Berlin]]
| Brandenburg = [[Bild:Brandenburg Wappen.svg|20px]] [[Liste der Bahnhöfe in Brandenburg]]
| Bremen = [[Bild:Bremen Wappen frei.svg|20px]] [[Bremen (Land)#Liste der Bahnhöfe in Bremen|Liste der Bahnhöfe in Bremen]]
| Hamburg = [[Bild:Coat of arms of Hamburg.svg|20px]] [[Liste Hamburger Bahnhöfe]]
| Hessen = [[Bild:Coat of arms of Hesse.svg|20px]] [[Liste der Bahnhöfe in Hessen]] bzw. [[Liste der SPNV-Stationen in Hessen]]
| Mecklenburg-Vorpommern = [[Bild:Coat of arms of Mecklenburg-Western Pomerania (small).svg|20px]] [[Eisenbahnlinien in Mecklenburg-Vorpommern#Bahnhöfe|Liste der Bahnhöfe in Mecklenburg-Vorpommern]]
| Niedersachsen = [[Bild:Coat of arms of Lower Saxony.svg|20px]] [[Liste der Bahnhöfe in Niedersachsen]]
| Nordrhein-Westfalen = [[Bild:Coat of arms of North Rhine-Westfalia.svg|20px]] [[Liste der Bahnhöfe in Nordrhein-Westfalen]]
| Rheinland-Pfalz =[[Bild:Coat of arms of Rhineland-Palatinate.svg|20px]] [[Liste der Bahnhöfe in Rheinland-Pfalz]]
| Saarland = [[Bild:Coa de-saarland 300px.png|20px]] [[Saarland#Bahnhofskategorien|Liste der Bahnhöfe im Saarland]]
| Sachsen-Anhalt = [[Bild:Wappen Sachsen-Anhalt.svg|20px]] [[Liste der Bahnhöfe in Sachsen-Anhalt]]
| Sachsen =[[Bild:Coat of arms of Saxony.svg|20px]] [[Liste der Bahnhöfe in Sachsen]]
| Schleswig-Holstein =[[Bild:Coat of arms of Schleswig-Holstein.svg|20px]] [[Liste der Bahnhöfe in Schleswig-Holstein]]
| Thüringen = [[Bild:Coat of arms of Thuringia.svg|20px]] [[Liste der Bahnhöfe in Thüringen]]
}}
|-
!colspan="2" style="text-align: center;" class="hintergrundfarbe6" |{{#switch: {{{Staat}}}
| Niederlande = [[Bild:Nl-arms.gif|20px]] [[Liste der Bahnhöfe in den Niederlanden]]
}}
|}
Test

Ordovizisches Massenaussterben

2006-12-13T05:39:27Z

Simetrical: «"-" → "–"»

[[Image:Extinction Intensity.png|thumb|300px|right|The Ordovician-Silurian extinction event, labeled "End O" here.]]
The '''Ordovician-Silurian extinction event''' was the second largest of the five major [[extinction event]]s in [[Earth]]'s history in terms of percentage of [[genus|genera]] that went extinct.

== History ==
The extinctions occurred approximately 444–447 million years ago and mark the boundary between the [[Ordovician Period|Ordovician]] and the following [[Silurian Period]]s. During this extinction event, which may have been composed of several distinct closely spaced events, there were several marked changes in biologically responsive [[carbon]] and [[oxygen]] [[isotope]]s, which may indicate separate events or particular phases within one event.

At that time all complex [[multicellular organism]]s lived in the sea, and around 100 marine [[Scientific classification|families]] became extinct, covering about 49%{{ref|Rohde2005}} of [[genus|genera]] of [[fauna (animals)|fauna]] (a more reliable estimate than species). The [[brachiopod]]s and [[bryozoan]]s were decimated, along with many of the [[trilobite]], [[conodont]] and [[graptolite]] families.

== Possible causes ==
These extinctions are currently being intensively studied; the most commonly accepted theory is that they were triggered by the onset of a long [[ice age]], perhaps the most severe glacial age of the [[Phanerozoic]], in the [[Hirnantian]] faunal stage that ended the long, stable [[Greenhouse effect|greenhouse]] conditions typical of the Ordovician. The event was preceded by a fall in atmospheric [[carbon dioxide|CO2]] which selectively affected the shallow [[sea]]s where most organisms lived.

As the southern [[supercontinent]] [[Gondwana]] drifted over the [[South Pole]], [[ice cap]]s formed on it. The strata have been detected in late Ordovician [[stratum|rock strata]] of North [[Africa]] and then-adjacent northeastern [[South America]], which were south-polar locations at the time. [[Glaciation]] locks up water from the world-ocean, and the [[interglacial]]s free it, causing [[sea level change|sea levels repeatedly to drop and rise]]; the vast shallow intra-continental Ordovician seas withdrew, which eliminated many [[ecological niche]]s, then returned, carrying diminished [[founder population]]s lacking many whole families of organisms. Then they withdrew again with the next pulse of glaciation, eliminating biological diversity at each change (Emiliani 1992 p. 491). In the North African strata, Julien Moreau reported five pulses of glaciation from [[seismic]] sections ([http://www.palass.org/pages/archive/News57a.pdf] IGCP meeting September 2004 reports pp 26f).

This incurred a shift in the location of bottom water formation, shifting from low [[latitude]]s, characteristic of greenhouse conditions, to high latitudes, characteristic of icehouse conditions, which was accompanied by increased deep-ocean currents and oxygenation of the bottomwater. An opportunistic fauna briefly thrived there, before anoxic conditions returned. The breakdown in the oceanic circulation patterns brought up nutrients from the abyssal waters. Surviving species were those that coped with the changed conditions and filled the [[ecological niche]]s left by the extinctions.

=== Gamma Ray Burst Hypothesis ===
Scientists from the [[University of Kansas]] and [[NASA]] have suggested that the initial extinctions could have been caused by a [[gamma ray burst]] originating from an exploding star within 6,000 light years of Earth (within a nearby arm of the [[Milky Way Galaxy]]). A ten-second burst would have stripped the Earth's atmosphere of half of its [[ozone]] almost immediately, causing surface-dwelling organisms, including those responsible for planetary [[photosynthesis]], to be exposed to high levels of [[ultraviolet]] radiation. This would have killed many species and caused a drop in temperatures [http://news.bbc.co.uk/1/hi/sci/tech/4433963.stm]. While plausible, there is no unambiguous evidence that such a nearby gamma ray burst has ever actually occurred.

== End of the event ==
The end of the second event occurred when melting glaciers caused the sea level to rise and stabilise once more. The rebound of life's diversity with the permanent reflooding of continental shelves at the onset of the Silurian saw increased biodiversity within the surviving [[order (biology)|orders]].

A major current (2004–2008) project of UNESCO's [[International Geoscience Programme]] (IGCP), following a successful probe of the Ordovician biodiversification, has as its major objective to seek the possible physical and chemical causes, related to changes in climate, sea level, volcanism, plate movements, extraterrestrial influences, of the Ordovician biodiversification, this end-Ordovician extinction, and the ensuing Silurian radiation [http://sarv.gi.ee/igcp503/IGCP503/index.html].

== See also ==
* [[Doomsday event]]
* [[Permian-Triassic extinction event]]

== Sources ==
*[[Cesare Emiliani|Emiliani, Cesare]], 1992. ''Planet Earth : Cosmology, Geology and the Evolution of Life and Environment''
*{{note|Rohde2005}} {{cite journal|author=Rohde & Muller|year=2005|title=Cycles in Fossil Diversity|journal=Nature|volume=434|pages=208-210|id={{doi|10.1038/nature03339}}|issue=7030}}

== Further reading ==
*Gradstein, Felix, James Ogg, and Alan Smith, eds., 2004. ''A Geologic Time Scale 2004'' (Cambridge University Press).
*Hallam, A. and Paul B. Wignall, 1997. ''Mass extinctions and their aftermath'' (Oxford University Press).
*Webby, Barry D. and Mary L. Droser, eds., 2004. ''The Great Ordovician Biodiversification Event'' (Columbia University Press).

== External links ==
*[http://www.bio.uu.nl/~palaeo/Paleobiologie/Maastricht_verniers.doc Jacques Veniers, "The end-Ordovician extinction event"]: abstract of Hallam and Wignall, 1997.

[[Category:Extinction events]]
[[Category:History of climate]]
[[Category:Ordovician]]
[[Category:Silurian]]

[[es:Extinciones masivas del Ordovícico-Silúrico]]
[[pl:Wymieranie ordowickie]]

Ordovizisches Massenaussterben

2006-12-13T05:39:11Z

Simetrical: Regex dash fixer

[[Image:Extinction Intensity.png|thumb|300px|right|The Ordovician-Silurian extinction event, labeled "End O" here.]]
The '''Ordovician-Silurian extinction event''' was the second largest of the five major [[extinction event]]s in [[Earth]]'s history in terms of percentage of [[genus|genera]] that went extinct.

== History ==
The extinctions occurred approximately 444-447 million years ago and mark the boundary between the [[Ordovician Period|Ordovician]] and the following [[Silurian Period]]s. During this extinction event, which may have been composed of several distinct closely spaced events, there were several marked changes in biologically responsive [[carbon]] and [[oxygen]] [[isotope]]s, which may indicate separate events or particular phases within one event.

At that time all complex [[multicellular organism]]s lived in the sea, and around 100 marine [[Scientific classification|families]] became extinct, covering about 49%{{ref|Rohde2005}} of [[genus|genera]] of [[fauna (animals)|fauna]] (a more reliable estimate than species). The [[brachiopod]]s and [[bryozoan]]s were decimated, along with many of the [[trilobite]], [[conodont]] and [[graptolite]] families.

== Possible causes ==
These extinctions are currently being intensively studied; the most commonly accepted theory is that they were triggered by the onset of a long [[ice age]], perhaps the most severe glacial age of the [[Phanerozoic]], in the [[Hirnantian]] faunal stage that ended the long, stable [[Greenhouse effect|greenhouse]] conditions typical of the Ordovician. The event was preceded by a fall in atmospheric [[carbon dioxide|CO2]] which selectively affected the shallow [[sea]]s where most organisms lived.

As the southern [[supercontinent]] [[Gondwana]] drifted over the [[South Pole]], [[ice cap]]s formed on it. The strata have been detected in late Ordovician [[stratum|rock strata]] of North [[Africa]] and then-adjacent northeastern [[South America]], which were south-polar locations at the time. [[Glaciation]] locks up water from the world-ocean, and the [[interglacial]]s free it, causing [[sea level change|sea levels repeatedly to drop and rise]]; the vast shallow intra-continental Ordovician seas withdrew, which eliminated many [[ecological niche]]s, then returned, carrying diminished [[founder population]]s lacking many whole families of organisms. Then they withdrew again with the next pulse of glaciation, eliminating biological diversity at each change (Emiliani 1992 p. 491). In the North African strata, Julien Moreau reported five pulses of glaciation from [[seismic]] sections ([http://www.palass.org/pages/archive/News57a.pdf] IGCP meeting September 2004 reports pp 26f).

This incurred a shift in the location of bottom water formation, shifting from low [[latitude]]s, characteristic of greenhouse conditions, to high latitudes, characteristic of icehouse conditions, which was accompanied by increased deep-ocean currents and oxygenation of the bottomwater. An opportunistic fauna briefly thrived there, before anoxic conditions returned. The breakdown in the oceanic circulation patterns brought up nutrients from the abyssal waters. Surviving species were those that coped with the changed conditions and filled the [[ecological niche]]s left by the extinctions.

=== Gamma Ray Burst Hypothesis ===
Scientists from the [[University of Kansas]] and [[NASA]] have suggested that the initial extinctions could have been caused by a [[gamma ray burst]] originating from an exploding star within 6,000 light years of Earth (within a nearby arm of the [[Milky Way Galaxy]]). A ten-second burst would have stripped the Earth's atmosphere of half of its [[ozone]] almost immediately, causing surface-dwelling organisms, including those responsible for planetary [[photosynthesis]], to be exposed to high levels of [[ultraviolet]] radiation. This would have killed many species and caused a drop in temperatures [http://news.bbc.co.uk/1/hi/sci/tech/4433963.stm]. While plausible, there is no unambiguous evidence that such a nearby gamma ray burst has ever actually occurred.

== End of the event ==
The end of the second event occurred when melting glaciers caused the sea level to rise and stabilise once more. The rebound of life's diversity with the permanent reflooding of continental shelves at the onset of the Silurian saw increased biodiversity within the surviving [[order (biology)|orders]].

A major current (2004–2008) project of UNESCO's [[International Geoscience Programme]] (IGCP), following a successful probe of the Ordovician biodiversification, has as its major objective to seek the possible physical and chemical causes, related to changes in climate, sea level, volcanism, plate movements, extraterrestrial influences, of the Ordovician biodiversification, this end-Ordovician extinction, and the ensuing Silurian radiation [http://sarv.gi.ee/igcp503/IGCP503/index.html].

== See also ==
* [[Doomsday event]]
* [[Permian-Triassic extinction event]]

== Sources ==
*[[Cesare Emiliani|Emiliani, Cesare]], 1992. ''Planet Earth : Cosmology, Geology and the Evolution of Life and Environment''
*{{note|Rohde2005}} {{cite journal|author=Rohde & Muller|year=2005|title=Cycles in Fossil Diversity|journal=Nature|volume=434|pages=208-210|id={{doi|10.1038/nature03339}}|issue=7030}}

== Further reading ==
*Gradstein, Felix, James Ogg, and Alan Smith, eds., 2004. ''A Geologic Time Scale 2004'' (Cambridge University Press).
*Hallam, A. and Paul B. Wignall, 1997. ''Mass extinctions and their aftermath'' (Oxford University Press).
*Webby, Barry D. and Mary L. Droser, eds., 2004. ''The Great Ordovician Biodiversification Event'' (Columbia University Press).

== External links ==
*[http://www.bio.uu.nl/~palaeo/Paleobiologie/Maastricht_verniers.doc Jacques Veniers, "The end-Ordovician extinction event"]: abstract of Hallam and Wignall, 1997.

[[Category:Extinction events]]
[[Category:History of climate]]
[[Category:Ordovician]]
[[Category:Silurian]]

[[es:Extinciones masivas del Ordovícico-Silúrico]]
[[pl:Wymieranie ordowickie]]

Banksia epica

2006-12-08T05:07:58Z

Simetrical: Fix formatting

{{Taxobox
| color = lightgreen
| name = Banksia epica
| status = {{StatusSecure}}
| image = Banksia_epica_02_gnangarra.jpg
| image_caption = ''B. epica'' [[inflorescence]] and leaves.
| regnum = [[Plant]]ae
| divisio = [[flowering plant|Magnoliophyta]]
| classis = [[dicotyledon|Magnoliopsida]]
| ordo = [[Proteales]]
| familia = [[Proteaceae]]
| genus = ''[[Banksia]]''
| subgenus = [[Banksia subg. Banksia|''Banksia'' subg. ''Banksia'']]
| sectio = [[Banksia sect. Banksia|''Banksia'' sect ''Banksia'']]
| series = [[Banksia ser. Cyrtostylis|''Banksia'' ser. ''Cyrtostylis'']]
| species = '''''B. epica'''''
| binomial = ''Banksia epica''
| binomial_authority = [[Alex George|A.S.George]]
}}
'''''Banksia epica''''' is a [[species]] of [[shrub]] in the [[plant]] [[genus]] ''[[Banksia]]''. Recently discovered and little studied, it is known only from two populations in the remote south east of [[Western Australia]]. It grows as a spreading bushy shrub up to two metres (6 ft) high, with large creamy-yellow flower spikes. First collected in 1973 but not recognised as a new species until 1988, it is placed in ''Banksia'' [[Banksia subg. Banksia|subgenus ''Banksia'']], [[Banksia sect. Banksia|section ''Banksia'']], [[Banksia ser. Cyrtostylis|series ''Cyrtostylis'']].

==Description==
''B. epica'' grows as a spreading bushy shrub with many branches, from 30 centimetres (12 in) to 3½ metres (11½ ft) tall. The bark is grey and fissured. The leaves are wedge-shaped, 1½ to 5 centimetres (½–2 in) long and 6 to 15 millimetres (1/8–2/3 in) wide, with serrated [[Leaf#margins (edge)|margins]]. Flowers occur in ''Banksia'''s characteristic "flower spike", an [[inflorescence]] made up of hundreds of pairs of flowers densely packed in a [[helix|spiral]] round a woody axis. ''B. epica''<nowiki>'</nowiki>s flower spike is a creamy yellow colour, cylindrical, 9 to 17 centimetres tall and around 6 centimetres in diameter. The fruiting structure is a stout woody "cone" embedded with up to 50 [[follicle]]s, and has a hairy appearance caused by the persistence of old withered flower parts.<ref name="George 1999">{{cite encyclopedia | author = George, Alex S. | year = 1999 | title = Banksia | editor = Wilson, Annette | encyclopedia = Flora of Australia | volume = Volume 17B: Proteaceae 3: Hakea to Dryandra | pages = 175–251 | publisher = CSIRO Publishing / [[Australian Biological Resources Study]] | id = ISBN 0-643-06454-0}}</ref>

''B. epica'' has a very similar appearance to its close relative ''[[Banksia media|B. media]]'' (Southern Plains Banksia), which also occurs in the area. It differs from ''B. media'' in having slightly shorter leaves and larger flowers. In addition, the persistent flower parts on ''B. epica''<div/>'s fruiting structures are curled and point upwards, whereas they are straight and point downwards on ''B. media''.<ref name="Taylor 1988">{{cite book | author = Taylor, Anne and [[Stephen Hopper|Stephen D. Hopper]] | year = 1988 | title = [[The Banksia Atlas]] (Australian Flora and Fauna Series Number 8) | publisher = Australian Government Publishing Service | location = Canberra | id = ISBN 0-644-07124-9}}</ref>

==Taxonomy==
===Taxonomic history===
The first European to sight ''B. epica'' may have been the explorer [[Edward John Eyre]], who recorded sighting "stunted specimens" of ''Banksia'' as he was nearing the western edge of the [[Great Australian Bight]] on [[1 May]] [[1841]]:<ref name="George 1988">{{cite journal | author = George, Alex S. | year = 1988 | title = New taxa and notes on ''Banksia'' L.f. (Proteaceae) | journal = Nuytsia | volume = 6 | issue = 3 | pages = 309–317}}</ref>
:"One circumstance in our route to-day cheered me greatly, and led me shortly to expect some important and decisive change in the character and formation of the country. It was the appearance for the first time of the Banksia, a shrub which I had never before found to the westward of Spencer's Gulf, but which I knew to abound in the vicinity of King George's Sound, and that description of country generally. Those only who have looked out with the eagerness and anxiety of a person in my situation, to note any change in the vegetation or physical appearance of a country, can appreciate the degree of satisfaction with which I recognised and welcomed the first appearance of the Banksia. Isolated as it was amidst the scrub, and insignificant as the stunted specimens were that I first met with, they led to an inference that I could not be mistaken in, and added, in a tenfold degree, to the interest and expectation with which every mile of our route had now become invested."<ref name="Eyre 1845">{{cite book | author = [[Edward John Eyre|Eyre, Edward John]] | year = 1845 | title = Journals of Expeditions of Discovery into Central Australia, and Overland from Adelaide to King George's Sound, in the Years 1840-1: Sent by the Colonists of South Australia, with the Sanction and Support of the Government: Including an Account of the Manners and Customs of the Aborigines and the State of their Relations with Europeans | location = London | publisher = T. and W. Boone | url = http://onlinebooks.library.upenn.edu/webbin/gutbook/lookup?num=5346 | access-date = 2006-08-31}}</ref>
Eyre is thought to have been passing through the Toolinna Cove sand patch at the time of writing.<ref name="Nelson 1974">{{cite journal | author = [[Ernest Charles Nelson|E. Charles Nelson]] | year = 1974 | title = Disjunct plant distributions on the south-western Nullarbor Plain, Western Australia | journal = Journal of the Royal Society of Western Australia | volume = 57 | issue = 4 | pages = 105–117}}</ref> ''B. epica'' and ''B. media'' are the only ''Banksia'' species that occur at that location,<ref name="George 1999"/> and both have a habit and form that fulfills Eyre's description. As he did not collect specimens, so it is impossible to determine what species he saw.

The first herbarium collection of ''B. epica'' was not made until October 1973, when [[Ernest Charles Nelson]] visited Toolinna Cove to collect specimens for a taxonomic revision of ''[[Adenanthos]]''. He became interested in the disjunct plant distributions there, and ended up collecting specimens of a range of plant species.<ref name="Nelson 1974"/> On 22 October, he collected a specimen of ''B. epica'' in old flower, but he did not recognise it as a new species. It was lodged in the [[herbarium]] at [[Canberra]] labelled as ''B. media''.<ref name="George 1988"/>

In 1985, two volunteer field collectors for ''[[The Banksia Atlas]]'' project, John and Lalage Falconer of [[Esperance, Western Australia|Esperance]], collected at [[Point Culver]] and became convinced that the location contained three ''Banksia'' species rather than two. On [[9 January]] [[1986]] they returned to the location, collecting leaves and old flowers of what they thought was an undescribed species; however they were unable to collect fresh flowers or fruit because the species flowers only from April to June. The Falconers' specimens did indeed suggest that a new species had been discovered, but they were insufficient for formal publication. Early in May the following year, John Falconer drove over 2000 kilometres on unsealed tracks from [[Warburton, Western Australia|Warburton]] to Point Culver and back again, in order to collect fresh flowers and fruit of the purported new species.<ref name="Taylor 1988"/> Based on these specimens, [[Alex George]] begin preparing a formal description of the genus. During his research, he discovered that Nelson's Toolinna Cove specimen was also referrable to the undescribed species. In the absence of any genuine ''B. media'' specimens from Toolinna Cova, George inferred that only ''B. epica'' occurred there, and that Eyre must have sighted ''B. epica'' in 1841. In 1988, he published a formal description of the species, naming it ''Banksia epica'' in reference to the two "epic" journeys of Eyre and Falconer.<ref name="George 1988"/> Thus the full name for the species is '''''Banksia epica'' A.S.George'''.<ref name="APNI">{{cite encyclopedia | author = Chapman, Arthur D. | year = 1991 | title = Banksia integrifolia L.f. | encyclopedia = [http://www.anbg.gov.au/cgi-bin/apni Australian Plant Name Index] (Australian Flora and Fauna Series '''12—15''') | location = Canberra | publisher = Australian Government Publishing Service | url = http://www.anbg.gov.au/cgi-bin/apni?taxon_id=53463 | accessdate = 2006-12-01}}</ref> A 1991 survey subsequently found both ''B. epica'' and ''B. media'' at Toolinna Cove.

===Current treatment===
George placed ''B. epica'' in [[Banksia subg. Banksia|''Banksia'' subg. ''Banksia'']], because its inflorescences take the form of ''Banksia''<div/>'s characteristic flower spikes; [[Banksia sect. Banksia|''Banksia'' sect. ''Banksia'']] because of its straight [[style]]s; and [[Banksia ser. Cyrtostylis|''Banksia'' ser. ''Cyrtostylis'']] because it has slender flowers.<ref name="George 1988"/> Its closest relatives are ''[[Banksia praemorsa|B. praemorsa]]'' (Cut-leaf Banksia) and ''B. media'', both of which have shorter flowers and a smaller [[pollen-presenter]] than ''B. epica''. In addition, ''B. praemorsa'' differs in having a hairless [[perianth]], and ''B. media'' has larger, more undulate leaves.<ref name="George 1999"/> Recent [[cladistics|cladistic analyses]] of ''Banksia'' confirmed ''B. epica''<div/>'s placement in ''Cyrtostylis'' alongside ''B. praemorsa'' and ''B. media'', despite finding George's conception of ''Cyrtostylis'' to be "widely [[polyphyly|polyphyletic]]".<ref name="Thiele 1996">{{cite journal |first=Kevin|last=Thiele| coauthors = Pauline Y. Ladiges | year = 1996 | title = A Cladistic Analysis of Banksia (Proteaceae) | journal = Australian Systematic Botany |volume=9|issue=5 | pages = 661-733}}</ref>

''B. epica''<div/>'s placement within ''Banksia'' may be summarised as follows:
:'''Genus ''[[Banksia]]'''''
::'''Subgenus ''[[Banksia subg. Banksia|Banksia]]'''''
:::'''Section ''[[Banksia sect. Banksia|Banksia]]'''''
::::Series ''[[Banksia ser. Salicinae|Salicinae]]''
::::Series ''[[Banksia ser. Grandes|Grandes]]''
::::Series ''[[Banksia ser. Banksia|Banksia]]''
::::Series ''[[Banksia ser. Crocinae|Crocinae]]''
::::Series ''[[Banksia ser. Prostratae|Prostratae]]''
::::'''Series ''[[Banksia ser. Cyrtostylis|Cyrtostylis]]'''''
:::::''[[Banksia media|B. media]]'' - ''[[Banksia praemorsa|B. praemorsa]]'' - '''''B. epica''''' - ''[[Banksia pilostylis|B. pilostylis]]'' - ''[[Banksia attenuata|B. attenuata]]'' - ''[[Banksia ashbyi|B. ashbyi]]'' - ''[[Banksia benthamiana|B. benthamiana]]'' - ''[[Banksia audax|B. audax]]'' - ''[[Banksia lullfitzii|B. lullfitzii]]'' - ''[[Banksia elderiana|B. elderiana]]'' - ''[[Banksia rosserae|B. rosserae]]'' -''[[Banksia laevigata|B. laevigata]]'' - ''[[Banksia elegans|B. elegans]]'' - ''[[Banksia lindleyana|B. lindleyana]]''
::::Series ''[[Banksia ser. Tetragonae|Tetragonae]]''
::::Series ''[[Banksia ser. Bauerinae|Bauerinae]]''
::::Series ''[[Banksia ser. Quercinae|Quercinae]]''
:::Section ''[[Banksia coccinea|Coccinea]]''
:::Section ''[[Banksia sect. Oncostylis|Oncostylis]]''
::Subgenus ''[[Banksia subg. Isostylis|Isostylis]]''

==Distribution and habitat==
[[Image:B epica dist map alt gnangarra.png|thumb|140px|right|Distribution map for ''Banksia epica'']]
''B. epica'' is known only from two populations on the [[Nullarbor Plain]] near the western edge of the [[Great Australian Bight]]. The main population occurs about 30 kilometres west of [[Point Culver]]; there were over 2000 plants there when surveyed in June 1989. A smaller population occurs about 70 kilometres further east at [[Toolinna Cove]]; when surveyed in August 1991, this locality had around 350 plants. This latter population represents the easternmost limit of the western ''Banksia'' species; east of Toolinna Cove no ''Banksia'' species occurs for over 900 kilometres.

Both of the localities in which ''B. epica'' is known to occur are unusual in having [[cliff-top dune]]s of deep, white [[silica|siliceous]] [[sand]]. Cliff-top dunes are uncommon along the Great Australian Bight, and most sand on the Nullarbor is heavily [[calcareous]]. As ''Banksia'' species are intolerant of calcareous soils, and are not adapted to long range [[seed]] [[biological dispersal|dispersal]], these populations appear to be reproductively isolated. Nelson has suggested that there was once a continuous strip of siliceous sand along the coast, providing an extensive and unfragmented habitat for ''B. epica''; rises in the sea level had submerged this strip, leaving only the cliff-top dunes as suitable habitat. The fact that the resultant isolated populations have not perceptibly [[speciation|speciated]] since then suggests that the species has been fragmented for only a short time, perhaps only since the [[Last Glacial Maximum]].<ref name="Nelson 1974"/>

''B. media'' and ''B. epica'' are the only ''Banksia'' species to grow on alkaline soil.<ref name="Lamont 1996">{{cite journal | author = "Lamont, Byron B. and S. W. Connell | year = 1996 | title = Biogeography of Banksia in southwestern Australia | journal = Journal of Biogeography | volume = 23 | pages = 295–309}}</ref>

==Ecology==
''B. epica'' lacks a [[lignotuber]], so it is thought to be killed by fire. Like all ''Banksia'' species, however, it is adapted to release its aerial bank of seeds following a bushfire, and so regenerates rapidly. Known pollinators include the [[New Holland Honeyeater]] and the [[Yellow-rumped Thornbill]].<ref name="Craig 2001"/> However detailed observational studies of other banksia species have generally revealed a wide range of invertebrate and vertebrate pollinators involved.

Because so few populations are known, ''B. epica'' has been declared "Priority Two - Poorly Known Taxa" under the [[Wildlife Conservation Act 1950]]. It is not considered to be under threat, however, because both populations occur within the [[Nuytsland Nature Reserve]], and are undisturbed and healthy.<ref name="Craig 2001">{{cite book | author = Gillian F. Craig and Coates, David J. | year = 2001 | title = Declared Rare and Poorly Known Flora in the Esperance District | chapter = B. Priority 2 Taxa | location = Bentley, Western Australia | publisher = Department of Conservation and Land Management | id = {{ISSN|0816-9713}} | chapterurl = http://www.calm.wa.gov.au/plants_animals/watscu/pdf/flora/flora_mgt_plans/esperance_2000/esperance_pri2.pdf | accessdate = 2006-08-31}}</ref> Furthermore, the area in which it occurs is poorly surveyed, so it is possible that other populations exist.<ref name="Taylor 1988"/>

==Cultivation==
Cultivation of ''B. epica'' has been pioneered by Kevin Collins of the Banksia Farm in [[Albany, Western Australia]]. It has been grown there in loamy clay or sandy gravel, and has shown strong tolerance for alkaline soils. It has also been successfully grown in well drained beds for several years at the [[Australian National Botanic Gardens]] in [[Canberra]], suggesting that it may be hardy to east coast conditions.<ref name="ASGAP">{{cite web | title = Banksia epica | publisher = [[Association of Societies for Growing Australian Plants]] (ASGAP) | url = http://farrer.csu.edu.au/ASGAP/b-epi.html | accessdate = 2006-08-30}}</ref>
<ref>{{cite journal|author=Liber C|year=2002|title=''Banksia epica'', ''media'' & ''praemorsa'' in ANBG, Canberra|journal=Banksia Study Group Newsletter|volume=4|issue=1|pages=4|publisher=[ASGAP]|id=ISSN 1444-285X}}
</ref>

==References==
<references/>

==External links==
{{wikicommons}}
{{wikispecies|Banksia epica}}
*{{Flora of Western Australia|name=Banksia epica|f=090|level=s|id=10798}}
*{{Flora of Australia Online|name=Banksia epica|id=3433}}

[[Category:Banksia species by scientific name|Epica]]
[[Category:Flora of Western Australia|Banksia epica]]
[[fr:Banksia epica]]

0,999…

2006-10-18T03:45:20Z

Simetrical: /* top */ The caption is unnecessary and detracts from the image if anything.

[[Image:999 Perspective.png|300px|right]]
In [[mathematics]], '''0.999…''' (also denoted <math>0.\bar{9}</math> or <math>0.\dot{9}</math>) is a [[recurring decimal]] which is [[equality (mathematics)|exactly equal]] to [[1 (number)|1]]. In other words, the symbols 0.999… and 1 represent the same real number. Mathematicians have formulated a number of [[mathematical proof|proof]]s of this identity, which vary with their level of [[rigor]], preferred development of the real numbers, background assumptions, historical context and target audience.

The equality 0.999… = 1 has long been taught in textbooks, and in the last few decades, researchers of [[mathematics education]] have studied the reception of this equation among students, who often vocally reject the equality. Their reasoning may be based on the expectation that [[infinitesimal]] quantities should exist, that [[arithmetic]] may be broken, or simply that 0.999… should have a last 9. These ideas are false in the [[real number]]s, as can be proven by explicitly constructing the reals from the [[rational number]]s, and such constructions can also prove that 0.999… = 1 directly. At the same time, some of the intuitive phenomena can occur in other number systems. There are even systems in which an object which can reasonably be called "0.999…" is strictly [[less than]] 1.

That the number 1 has two [[decimal expansion]]s is not a peculiarity of the decimal system. The same phenomenon occurs in [[integer]] [[radix|base]]s other than 10, and mathematicians have also quantified the ways of writing 1 in non-integer bases. Nor is the phenomenon unique to 1: every terminating decimal expansion has a twin with trailing 9s. In fact, all [[positional numeral system]]s contain an infinity of ambiguous numbers. These various identities have been applied to better understand patterns in the decimal expansions of [[fraction (mathematics)|fraction]]s and the structure of a simple fractal, the [[Cantor set]]. They also occur in a classic investigation of the infinitude of the entire set of real numbers.

==Digit manipulation==
0.999… is a number written in [[decimal]] [[numeral system]], and some of the simplest proofs that 0.999… = 1 rely on the convenient [[arithmetic]] properties of this system. Most of decimal arithmetic — [[addition]], [[subtraction]], [[multiplication]], [[division (mathematics)|division]], and [[inequality|comparison]] — uses manipulations at the digit level that are much the same as those for [[integer]]s. And like integers, any two ''finite'' decimals with different digits mean different numbers (ignoring trailing zeros). In particular, any number of the form 0.99…9, where the 9s eventually stop, is strictly less than 1.

Unlike the case with integers and finite decimals, other notations can express a single number in multiple ways. For example, using [[fraction]]s,
:1⁄2 = 3⁄6.
Infinite decimals, however, can express the same number in at most two different ways. If there are two ways, then one of them must end with an infinite series of nines, and the other must terminate (that is, consist of a recurring series of zeroes from a certain point on).
=== Fraction proof ===
{|class="infobox" style="padding:.5em; border:1px solid #ccc" align="right" cellpadding="0" cellspacing="0"
|-
|align="right"| 0.333… || = 1⁄3
|-
|align="right"| 3 × 0.333… || = 3 × 1⁄3
|-
|align="right"| 0.999… || = 1
|}
One reason that infinite decimals are a necessary extension of finite decimals is to represent fractions. Using [[long division]], a simple division of integers like 1⁄3 becomes a [[recurring decimal]], 0.3333…, in which the digits repeat without end. This decimal yields a quick proof for 0.999…. Multiplication of 3 times 3 produces 9 in each digit, so 3 × 0.3333… equals 0.9999…. But 3 × 1⁄3 equals 1, so 0.9999… = 1.<ref name="CME">cf. with the binary version of the same argument in [[Martin Gardner]] and [[Silvanus P. Thompson]], ''Calculus made easy'', St. Martin's Press, New York, 1998. ISBN 0-312-18548-0.</ref>

=== Algebra proof ===
{|class="infobox" style="padding:.5em; border:1px solid #ccc" align="right" cellpadding="0" cellspacing="0"
|-
|align="right"| ''c'' || = 0.999…
|-
|align="right"| 10''c'' || = 9.999…
|-
|align="right"| 10''c'' − ''c'' || = 9.999… − 0.999…
|-
|align="right"| 9''c'' || = 9
|-
|align="right"| ''c'' || = 1
|}
Another kind of proof more easily adapts to other repeating decimals. When a fraction in decimal notation is multiplied by 10, the digits do not change but the decimal separator moves one place to the right. Thus 10 × 0.9999… equals 9.9999…, which is 9 more than the original number. To see this, consider that subtracting 0.9999… from 9.9999… can proceed digit by digit; the result is 9 − 9, which is 0, in each of the digits after the decimal separator. But trailing zeros do not change a number, so the difference is exactly 9. The final step uses algebra. Let the decimal number in question, 0.9999…, be called ''c''. Then 10''c'' − ''c'' = 9. This is the same as 9''c'' = 9. Dividing both sides by 9 completes the proof: ''c'' = 1.<ref name="CME"/>

== Calculus and analysis ==
Since the question of 0.999… does not affect the formal development of mathematics, it can be postponed until one proves the standard theorems of real analysis. Rigorous proofs are generally not studied before the university level.

One requirement is to characterize real numbers that can be written in decimal notation, consisting of an optional sign, a finite sequence of any number of digits forming an integer part, a decimal separator, and a sequence of digits forming a fractional part. For the purpose of discussing 0.999…, the integer part can be summarized as ''b''0 and one can neglect negatives, so a decimal expansion has the form
:''b''0.''b''1''b''2''b''3''b''4''b''5….

It is vital that the fraction part, unlike the integer part, is not limited to a finite number of digits. This is a [[positional notation]], so for example the 5 in 500 contributes ten times as much as the 5 in 50, and the 5 in 0.05 contributes one tenth as much as the 5 in 0.5.

===Infinite series and sequences===
Perhaps the most common development of decimal expansions is to define them as sums of [[infinite series]]. In general:
:<math>b_0 . b_1 b_2 b_3 b_4 \ldots = b_0 + b_1({\textstyle\frac{1}{10}}) + b_2({\textstyle\frac{1}{10}})^2 + b_3({\textstyle\frac{1}{10}})^3 + b_4({\textstyle\frac{1}{10}})^4 + \cdots .</math>

For 0.999… one can apply the powerful [[convergent series|convergence]] theorem concerning [[infinite geometric series]]:<ref>Rudin p.61, Theorem 3.26; J. Stewart p.706</ref>
:If <math>|r| < 1</math> then <math>ar+ar^2+ar^3+\cdots = \textstyle\frac{ar}{1-r}.</math>

Since 0.999… is such a sum with a common ratio <math>r=\textstyle\frac{1}{10}</math>, the theorem makes short work of the question:
:<math>0.999\ldots = 9({\textstyle\frac{1}{10}}) + 9({\textstyle\frac{1}{10}})^2 + 9({\textstyle\frac{1}{10}})^3 + \cdots = \frac{9({\textstyle\frac{1}{10}})}{1-{\textstyle\frac{1}{10}}} = 1.\,</math>
This proof (actually, that 10 equals "9·9999999, &c.") appears as early as 1770 in [[Leonard Euler]]'s ''[[Elements of Algebra]]''.<ref>Euler p.170</ref>

[[Image:base4 333.svg|left|thumb|200px|Limits: The unit interval, including the base-4 decimal sequence (.3, .33, .333, …) converging to 1.]]
The sum of a geometric series is itself a result even older than Euler. A typical 18th-century derivation used a term-by-term manipulation similar to the [[#Algebra proof|algebra proof]] given above, and as late as 1811, Bonnycastle's textbook ''An Introduction to Algebra'' uses such an argument for geometric series to justify the same maneuver on 0.999….<ref>Grattan-Guinness p.69; Bonnycastle p.177</ref> A 19th-century reaction against such liberal summation methods resulted in the definition that still dominates today: the sum of a series is defined to be the limit of the sequence of its partial sums. A corresponding proof of the theorem explicitly computes that sequence; it can be found in any proof-based introduction to calculus or analysis.<ref>For example, J. Stewart p.706, Rudin p.61, Protter and Morrey p.213, Pugh p.180, J.B. Conway p.31</ref>

A sequence (''x''0, ''x''1, ''x''2, …) has a [[limit of a sequence|limit]] ''x'' if the distance |''x'' − ''x''''n''| becomes arbitrarily small as ''n'' increases. The statement that 0.999… = 1 can itself be interpreted and proven as a limit:
:<math>0.999\ldots = \lim_{n\to\infty}0.\underbrace{ 99\ldots9 }_{n} = \lim_{n\to\infty}\left(1-\frac{1}{10^n}\right) = 1-\lim_{n\to\infty}\frac{1}{10^n} = 1.</math><ref>The limit follows, for example, from Rudin p. 57, Theorem 3.20e. For a more direct approach, see also Finney, Weir, Giordano (2001) ''Thomas' Calculus: Early Transcendentals'' 10ed, Addison-Wesley, New York. Section 8.1, example 2(a), example 6(b).</ref>

The last step -- that lim 1/10''n'' = 0 -- is often justified by the axiom that the real numbers have the [[Archimedean property]]. This limit-based attitude towards 0.999… is often put in more evocative but less precise terms. For example, the 1846 textbook ''The University Arithmetic'' explains, ".999 +, continued to infinity = 1, because every annexation of a 9 brings the value closer to 1"; the 1895 ''Arithmetic for Schools'' says, "...when a large number of 9s is taken, the difference between 1 and .99999… becomes inconceivably small".<ref>Davies p.175; Smith and Harrington p.115</ref> Such heuristics are often interpreted by students as implying that 0.999… itself is less than 1; see [[#Skepticism in education|below]].

===Nested intervals and least upper bounds===
[[Image:999 Intervals C.svg|right|thumb|Nested intervals: in base 3, 1 = 1.000… = 0.222…]]
The series definition above is a simple way to define the real number named by a decimal expansion. A complementary approach is tailored to the opposite process: for a given real number, define the decimal expansion(s) that are to name it.

If a real number ''x'' is known to lie in the [[closed interval]] [0, 10] (i.e., it is greater than or equal to 0 and less than or equal to 10), one can imagine dividing that interval into ten pieces that overlap only at their endpoints: [0, 1], [1, 2], [2, 3], and so on up to [9, 10]. The number ''x'' must belong to one of these; if it belongs to [2, 3] then one records the digit "2" and subdivides that interval into [2, 2.1], [2.1, 2.2], …, [2.8, 2.9], [2.9, 3]. Continuing this process yields an infinite sequence of [[nested intervals]], labelled by an infinite sequence of digits ''b''0, ''b''1, ''b''2, ''b''3, …, and one writes
:''x'' = ''b''0.''b''1''b''2''b''3…

In this formalism, the fact that 1 = 1.000… and also 1 = 0.999… reflects the fact that 1 lies in both [0, 1] and [1, 2], so one can choose either subinterval when finding its digits. To ensure that this notation does not abuse the "=" sign, one needs a way to reconstruct a unique real number for each decimal. This can be done with limits, but other constructions continue with the ordering theme.<ref>Beals p.22; I. Stewart p.34</ref>

One straightforward choice is the [[Nested Intervals Theorem]], which guarantees that given a sequence of nested, closed intervals whose lengths become arbitrarily small, the intervals contain exactly one real number in their [[intersection (set theory)|intersection]]. So ''b''0.''b''1''b''2''b''3… is defined to be the unique number contained within all the intervals [''b''0, ''b''0 + 1], [''b''0.''b''1, ''b''0.''b''1 + 0.1], and so on. 0.999… is then the unique real number that lies in all of the intervals [0, 1], [0.9, 1], [0.99, 1], and [0.99…9, 1] for every finite string of 9s. Since 1 is an element of each of these intervals, 0.999… = 1.<ref>Bartle and Sherbert pp.60-62; Pedrick p.29; Sohrab p.46</ref>

The Nested Intervals Theorem is usually founded upon a more fundamental characteristic of the real numbers: the existence of [[least upper bound]]s or ''suprema''. To directly exploit these objects, one may define ''b''0.''b''1''b''2''b''3… to be the least upper bound of the set of approximants {''b''0, ''b''0.''b''1, ''b''0.''b''1''b''2, …}.<ref>Apostol pp.9, 11-12; Beals p.22; Rosenlicht p.27</ref> One can then show that this definition (or the nested intervals definition) is consistent with the subdivision procedure, implying 0.999… = 1 again. Tom Apostol concludes,
:"The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum."<ref>Apostol p.12</ref>

== Skepticism in education ==
Students of mathematics often reject the equality of 0.999… and 1 for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of [[infinitesimal]]s. There are many common contributing factors to the confusion:
*Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.<ref>Bunch p.119; Tall and Schwarzenberger p.6. The last suggestion is due to Burrell (p.28): "Perhaps the most reassuring of all numbers is 1. ...So it is particularly unsettling when someone tries to pass off 0.9~ as 1."</ref>
*Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 at infinity.<ref>Tall and Schwarzenberger pp.6-7; Tall 2001 p.221</ref>
*Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since the sequence never reaches its limit. Those who accept the difference between a sequence of numbers and its limit might read "0.999…" as meaning the former rather than the latter.<ref>Tall and Schwarzenberger p.6; Tall 2001 p.221</ref>
These ideas are mistaken in the context of the standard real numbers, although many of them are partially borne out in more sophisticated structures, either invented for their general mathematical utility or as instructive [[counterexample]]s to better understand 0.999….

Many of these explanations were found by professor David Tall, who has studied characteristics of teaching and cognition that lead to some of the misunderstandings he has encountered in his college students. Interviewing his students to determine why the vast majority initially rejected the equality, he found that "students continued to conceive of 0.999… as a sequence of numbers getting closer and closer to 1 and not a fixed value, because 'you haven’t specified how many places there are' or 'it is the nearest possible decimal below 1'".<ref>Tall 2001 p.221</ref>

Of the elementary proofs, multiplying 0.333… = 1/3 by 3 is apparently a successful strategy for convincing reluctant students that 0.999… = 1. Still, when confronted with the conflict between their belief of the first equation and their disbelief of the second, some students either begin to disbelieve the first equation or simply become frustrated.<ref>Tall 1976 pp.10-14</ref> Nor are more sophisticated methods foolproof: students who are fully capable of applying rigorous definitions may still fall back on intuitive images when they are surprised by a result in advanced mathematics, including 0.999…. For example, one real analysis student was able to prove that 0.333… = 1/3 using a supremum definition, but then insisted that 0.999… < 1 based on her earlier understanding of long division.<ref>Pinto and Tall p.5, Edwards and Ward pp.416-417</ref>

Joseph Mazur tells the tale of an otherwise brilliant calculus student of his who "challenged almost everything I said in class but never questioned his calculator," and who had come to believe that nine digits are all one needs to do mathematics, including calculate the square root of 23. The student remained uncomfortable with a limiting argument that 9.99… = 10, calling it a "wildly imagined infinite growing process."<ref>Mazur pp.137-141</ref>

As part of Ed Dubinsky's "APOS theory" of mathematical learning, Dubinsky and his collaborators (2005) propose that students who conceive of 0.999… as a finite, indeterminate string with an infinitely small distance from 1 have "not yet constructed a complete process conception of the infinite decimal". Other students who have a complete process conception of 0.999… may not yet be able to "encapsulate" that process into an "object conception", like the object conception they have of 1, and so they view the process 0.999… and the object 1 as incompatible. Dubinsky ''et al.'' also link this mental ability of encapsulation to viewing 1/3 as a number in its own right and to dealing with the set of natural numbers as a whole.<ref>Dubinsky ''et al.'' 261-262</ref>

== The real numbers ==
Other approaches explicitly define real numbers to be certain [[construction of real numbers|structures built upon the rational numbers]], using [[axiomatic set theory]]. The [[natural number]]s — 0, 1, 2, 3, and so on — begin with 0 and continue upwards, so that every number has a successor. One can extend the natural numbers with their negatives to give all the [[integer]]s, and to further extend to ratios, giving the [[rational number]]s. These number systems are accompanied by the arithmetic of addition, subtraction, multiplication, and division. More subtly, they include [[order theory|ordering]], so that one number can be compared to another and found less than, greater than, or equal. Two numbers (which are now sets) are [[equality (mathematics)|equal]] if and only if they have the same elements.

The step from rationals to reals is a huge extension, and there are at least two popular ways to achieve the step, both published in 1872: Dedekind cuts and Cauchy sequences. Proofs that 0.999… = 1 that directly use these constructions are not found in textbooks on real analysis, where the modern trend for the last few decades has been to use an axiomatic analysis. Even when a construction is offered, it is usually applied towards proving the axioms of the real numbers, which then support the above proofs. However, several authors express the idea that starting with a construction is more logically appropriate, and the resulting proofs are more self-contained.<ref>The historical synthesis is claimed by Griffiths and Hilton (p.xiv) in 1970 and again by Pugh (p.10) in 2001; both actually prefer Dedekind cuts to axioms. For the use of cuts in textbooks, see Pugh p.17 or Rudin p.17. For viewpoints on logic, Pugh p.10, Rudin p.ix, or Munkres p.30</ref> The following two examples come from rather unique sources.

=== Dedekind cuts ===
In the [[Dedekind cut]] approach, each real number ''x'' is the infinite set of all rational numbers that are less than ''x''.<ref>Enderton (p.113) qualifies this description: "The idea behind Dedekind cuts is that a real number ''x'' can be named by giving an infinite set of rationals, namely all the rationals less than ''x''. We will in effect define ''x'' to be the set of rationals smaller than ''x''. To avoid circularity in the definition, we must be able to characterize the sets of rationals obtainable in this way…"</ref> In particular, the real number 1 is the set of all rational numbers that are less than 1.<ref>Rudin pp.17-20, Richman p.399, or Enderton p.119. To be precise, Rudin, Richman, and Enderton call this cut 1*, 1−, and 1''R'', respectively; all three identify it with the traditional real number 1. Note that what Rudin and Enderton call a Dedekind cut, Richman calls a "nonprincipal Dedekind cut".</ref> Every positive decimal expansion easily determines a Dedekind cut: the set of rational numbers which are less than some stage of the expansion. So the real number 0.999… is the set of rational numbers ''r'' such that ''r'' < 0, or ''r'' < 0.9, or ''r'' < 0.99, or ''r'' is less than some other number of the form 1 − (1⁄10)''n''.<ref>Richman p.399</ref> Every element of 0.999… is less than 1, so it is an element of the real number 1. Conversely, an element of 1 is a rational number ''a''/''b'' < 1, which implies ''a''/''b'' < 1 − (1⁄10)''b''. Since 0.999… and 1 contain the same rational numbers, they are the same set: 0.999… = 1.

The definition of real numbers as Dedekind cuts was first published by [[Richard Dedekind]] in 1872.<ref name="MacTutor2">{{cite web |url=http://www-gap.dcs.st-and.ac.uk/~history/PrintHT/Real_numbers_2.html |title=History topic: The real numbers: Stevin to Hilbert |author=J J O'Connor and E F Robertson |work=MacTutor History of Mathematics |date=October 2005 |accessdate=2006-08-30}}</ref>
The above approach to assigning a real number to each decimal expansion is due to an expository paper titled "Is 0.999 … = 1?" by Fred Richman in ''[[Mathematics Magazine]]'', which is targeted at [[undergraduate]] mathematicians.<ref>{{cite web |url=http://www.maa.org/pubs/mm-guide.html |title=Mathematics Magazine:Guidelines for Authors |publisher=[[The Mathematical Association of America]] |accessdate=2006-08-23}}</ref> Richman notes that taking Dedekind cuts in any [[dense subset]] of the rational numbers yields the same results; in particular, he uses [[decimal fraction]]s, for which the proof is more immediate: "So we see that in the traditional definition of the real numbers, the equation 0.9* = 1 is built in at the beginning."<ref>Richman pp.398-399</ref> A further modification of the procedure leads to a different structure that Richman is more interested in describing; see "[[#Other number systems|Other number systems]]" below.

=== Cauchy sequences ===
Another approach to constructing the real numbers uses the ordering of rationals less directly. First, the distance between ''x'' and ''y'' is defined as the absolute value |''x'' − ''y''|, where |''z''| is the maximum of ''z'' and −''z'', thus never negative. Then the reals are defined to be the sequences of rationals that are [[Cauchy sequence|Cauchy]] using this distance. That is, in the sequence (''x''0, ''x''1, ''x''2, …), a mapping from natural numbers to rationals, for any positive rational δ there is an ''N'' such that |''x''''m'' − ''x''''n''| ≤ δ for all ''m'', ''n'' > ''N''. (The distance between terms becomes arbitrarily small.)<ref>Griffiths & Hilton §24.2 "Sequences" p.386</ref>

If (''x''''n'') and (''y''''n'') are two Cauchy sequences, then they are defined to be equal as real numbers if the sequence (''x''''n'' − ''y''''n'') has the limit 0. Truncations of the decimal number ''b''0.''b''1''b''2''b''3… generate a sequence of rationals which is Cauchy; this is taken to define the real value of the number.<ref>Griffiths & Hilton pp.388, 393</ref> Thus in this formalism the task is to show that the sequence of rational numbers

:<math>\left(1 - 0, 1 - {9 \over 10}, 1 - {99 \over 100}, \dots\right)
= \left(1, {1 \over 10}, {1 \over 100}, \dots \right)</math>

has the limit 0. Considering the ''n''th term of the sequence, for ''n''=0,1,2,…, it must therefore be shown that

:<math>\lim_{n\rightarrow\infty}\frac{1}{10^n} = 0.</math>

This limit is plain;<ref>Griffiths & Hilton pp.395</ref> one possible proof is that for ε = ''a''/''b'' > 0 one can take ''N'' = ''b'' in the definition of the [[limit of a sequence]]. So again 0.9999… = 1.

The definition of real numbers as Cauchy sequences was first published separately by [[Eduard Heine]] and [[Georg Cantor]], also in 1872.<ref name="MacTutor2" /> The above approach to decimal expansions, including the proof that 0.999… = 1, closely follows Griffiths & Hilton's 1970 work ''A comprehensive textbook of classical mathematics: A contemporary interpretation''. The book is written specifically to offer a second look at familiar concepts in a contemporary light.<ref>Griffiths & Hilton pp.viii, 395</ref>

==Other number systems==
Although the real numbers form an extremely useful number system, the decision to interpret the phrase "0.999…" as naming a real number is ultimately a convention, and Timothy Gowers argues in ''Mathematics: A Very Short Introduction'' that the resulting identity 0.999… = 1 is a convention as well:
:"However, it is by no means an arbitrary convention, because not adopting it forces one either to invent strange new objects or to abandon some of the familiar rules of arithmetic."<ref>Gowers p.60</ref>

One can place constraints on hypothetical number systems where 0.999… ≠ 1, with their new objects and/or unfamiliar rules, by reinterpreting the above proofs. As Richman puts it, "one man's proof is another man's ''[[reductio ad absurdum]]''."<ref>Richman p.396; emphasis is his. This line appears in a paragraph of the published version that is not present in the earlier preprint.</ref> If 0.999… is to be different from 1, then at least one of the assumptions built into the proofs must break down.

===Infinitesimals===
Some proofs that 0.999… = 1 rely on the [[Archimedean property]] of the standard real numbers: there are no nonzero [[infinitesimal]]s. There are mathematically coherent ordered [[algebraic structure]]s, including various alternatives to standard reals, which are non-Archimedean. For example, the [[dual number]]s include a new infinitesimal element ε, analogous to the imaginary unit ''i'' in the [[complex number]]s except that ε2 = 0. The resulting structure is useful in [[automatic differentiation]]. The dual numbers can be given a [[lexicographic order]], in which case the multiples of ε become non-Archimedean elements.<ref>Berz 439-442</ref> Another way to construct alternatives to standard reals is to use [[topos]] theory and alternative logics rather than [[set theory]] and classical logic (which is a special case). For example, [[smooth infinitesimal analysis]] has infinitesimals with no [[Multiplicative inverse|reciprocal]]s.<ref>{{cite paper|url=http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf|title=An Invitation to Smooth Infinitesimal Analysis|author=John L. Bell |year=2003 |format=PDF |accessdate=2006-06-29}}</ref>

[[Non-standard analysis]] is well-known for including a number system with a full array of infinitesmals (and their inverses) which provide a different, and perhaps more intuitive, approach to [[calculus]].<ref>For a full treatment of non-standard numbers see for example Robinson's ''Non-standard Analysis''.</ref> A.H. Lightstone provided a development of non-standard decimal expansions in 1972 in which every extended real number in (0, 1) has a unique extended decimal expansion: a sequence of digits 0.ddd…;…ddd… indexed by the extended natural numbers. In his formalism, there are two natural extensions of 0.333…, neither of which falls short of 1/3 by an infinitesimal:
:0.333…;…000… does not exist, while
:0.333…;…333… = 1/3 exactly.<ref>Lightstone pp.245-247. He does not explore the possibility repeating 9s in the standard part of an expansion.</ref>

[[Combinatorial game theory]] provides alternative reals as well, with infinite Blue-Red [[Hackenbush]] as one particularly relevant example. In 1974, [[Elwyn Berlekamp]] described a correspondence between Hackenbush strings and binary expansions of real numbers, motivated by the idea of [[data compression]]. For example, the value of the Hackenbush string LRRLRLRL… is 0.010101… = 1/3. However, the the value of LRLLL… (corresponding to 0.111…) is infinitesimally less than 1. The difference between the two is the [[surreal number]] 1/ω, where ω is the first [[ordinal number|infinite ordinal]]; the relevant game is LRRRR… or 0.000….<ref>Berlekamp, Conway, and Guy (pp.79-80, 307-311) discuss 1 and 1/3 and touch on 1/ω. The game for 0.111… follows directly from Berlekamp's Rule, and it is discussed by {{cite web |url=http://www.maths.nott.ac.uk/personal/anw/Research/Hack/ |title=Hackenstrings and the 0.999… ≟ 1 FAQ |author=A. N. Walker |year=1999 |accessdate=2006-06-29}}</ref>

===Breaking subtraction===
Another way that the proofs might be undermined is if 1 − 0.999… simply does not exist, because subtraction is not always possible. Mathematical structures with an addition operation but not a subtraction operation include [[commutative semigroup]]s, [[commutative monoid]]s and [[semiring]]s. Richman considers two such systems, designed so that 0.999… < 1.

First, Richman defines a nonnegative ''decimal number'' to be nothing more or less than a literal decimal expansion. He defines the [[lexicographical order]] and an addition operation, noting that 0.999… < 1 simply because 0 < 1 in the ones place, but for any nonterminating ''x'', one has 0.999… + ''x'' = 1 + ''x''. So one peculiarity of the decimal numbers is that addition cannot always be cancelled; another is that no decimal number corresponds to 1⁄3. After defining multiplication, the decimal numbers form a positive, totally ordered, commutative semiring.<ref>Richman pp.397-399</ref>

During the definition of multiplication Richman defines another system he calls "cut ''D''", which is the set of Dedekind cuts of decimal fractions. Ordinarily this definition leads to the real numbers, but for a decimal fraction ''d'' he allows both the cut (−∞, d) and the "principal cut" (−∞, d]. The result is that the real numbers are "living uneasily together with" the decimal fractions. Again 0.999… < 1. There are no positive infinitesimals in cut ''D'', but there is "a sort of negative infinitesimal", 0−, which has no decimal expansion. He concludes that 0.999… = 1 + 0−, while the equation "0.999… + ''x'' = 1"
has no solution.<ref>Richman pp.398-400. Rudin (p.23) assigns this alternate construction (but over the rationals) as the last exercise of Chapter 1.</ref>

===''p''-adic numbers===
When asked what 1 − 0.999… might be, students often invent the number "0.000…1". Whether or not that makes sense, the intuitive goal is clear: adding a 1 to the last 9 in 0.999… would carry all the 9s into 0s and leave a 1 in the ones place. Among other reasons, this idea fails because there is no "last 9" in 0.999….<ref>Gardiner p.98; Gowers p.60</ref> For an infinite string of 9s including a last 9, one must look elsewhere.

[[Image:4adic 333.svg|right|thumb|200px|The 4-adic integers (black points), including the sequence (3, 33, 333, …) converging to −1. The 10-adic analogue is …999 = −1.]]
The [[p-adic number|''p''-adic number]]s are an alternate number system of interest in [[number theory]]. Like the real numbers, the ''p''-adic numbers can be built from the rational numbers via [[Cauchy sequence]]s; the construction uses a different metric in which 0 is closer to ''p'', and much closer to ''pn'', than it is to 1 . The ''p''-adic numbers form a field for prime ''p'' and a [[ring (mathematics)|ring]] for other ''p'', including 10. So arithmetic can be performed in the ''p''-adics, and there are no infinitesimals.

In the 10-adic numbers, the analogues of decimal expansions run to the left. The 10-adic expansion …999 does have a last 9, and it does not have a first 9. One can add 1 to the ones place, and it leaves behind only 0s after carrying through: 1 + …999 = …000 = 0, and so …999 = −1.<ref name="Fjelstad11">Fjelstad p.11</ref> Another derivation uses a geometric series. The infinite series implied by "…999" does not converge in the real numbers, but it converges in the 10-adics, and so one can re-use the familiar formula:
:<math>\ldots999 = 9 + 9(10) + 9(10)^2 + 9(10)^3 + \ldots = \frac{9}{1-10} = -1.</math><ref>Fjelstad pp.14-15</ref>
(Compare with the series [[#Infinite series and sequences|above]].) A third derivation was invented by a seventh-grader who was doubtful over her teacher's limiting argument that 0.999… = 1 but was inspired to take the multiply-by-10 proof [[#Algebra proof|above]] in the opposite direction: if ''x'' = …999 then 10''x'' = ''x'' − 9, hence ''x'' = −1 again.<ref name="Fjelstad11" />

As a final extension, since 0.999… = 1 (in the reals) and …999 = −1 (in the 10-adics), then by "blind faith and unabashed juggling of symbols"<ref>DeSua p.901</ref> one may add the two equations and arrive at …999.999… = 0. This equation does not make sense either as a 10-adic expansion or an ordinary decimal expansion, but it turns out to be meaningful and true if one develops a theory of "double-decimals" with eventually-repeating left ends to represent a familiar system: the real numbers.<ref>DeSua pp.902-903</ref>

==Generalizations==
Proofs that 0.999… = 1 immediately generalize in two ways. First, every nonzero number with a finite decimal notation (equivalently, endless trailing 0s) has a [[doppelgänger]] with trailing 9s. For example, 0.24999… equals 0.25, exactly as in the special case considered. These numbers are exactly the decimal fractions, and they are dense.<ref>Petkovšek p.408</ref>

Second, a comparable theorem applies in each radix or [[base (mathematics)|base]]. For example, in base 2 (the [[binary numeral system]]) 0.111… equals 1, and in base 3 (the [[ternary numeral system]]) 0.222… equals 1. Textbooks of real analysis are likely to skip the example of 0.999… and present one or both of these generalizations from the start.<ref>Protter and Morrey p.503; Bartle and Sherbert p.61</ref>

Alternate representations of 1 also occur in non-integer bases. For example, in the [[golden ratio base]], the two standard representations are 1.000… and 0.101010…, and there infinitely many more representations that include adjacent 1s. Generally, for [[almost all]] ''q'' between 1 and 2, there are uncountably many base-''q'' expansions of 1. On the other hand, there are still uncountably many ''q'' (including 2 and 10) for which there is only one base-''q'' expansion of 1, other than the trivial 1.000…. This result was first obtained by [[Paul Erdős]], Miklos Horváth, and István Joó around 1990. In 1998 Vilmos Komornik and Paola Loreti determined the smallest such base, ''q'' = 1.787231650…. In this base, 1 = 0.11010011001011010010110011010011…; the digits are given by the [[Thue-Morse sequence]], which does not repeat.<ref>Komornik and Loreti p.636</ref>

A more far-reaching generalization addresses [[non-standard positional numeral systems|the most general positional numeral systems]]. They too have multiple representations, and in some sense the difficulties are even worse. For example:<ref>Kempner p.611; Petkovšek p.409</ref>
*In the [[balanced ternary]] system, 1/2 = 0.111… = 1.111….
*In the [[factoradic]] system, 1 = 1.000… = 0.1234….
Marko Petkovšek has proved that such ambiguities are necessary consequences of using a positional system: for any system that names all the real numbers, the set of reals with multiple representations is always dense. He calls the proof "an instructive exercise in elementary [[point-set topology]]"; it involves viewing sets of positional values as [[Stone space]]s and noticing that their real representations are given by [[continuous function (topology)|continuous functions]].<ref>Petkovšek pp.410-411</ref>

==Applications==
One application of 0.999… as a representation of 1 occurs in [[elementary number theory]]. In 1802, an H. Goodwin published an observation on the appearance of 9s in the repeating-decimal representations of fractions whose denominators are certain [[prime number]]s. Examples include:
*1/7 = 0.142857142857… and 142 + 857 = 999.
*1/73 = 0.0136986301369863… and 0136 + 9863 = 9999.
E. Midy proved a general result about such fractions, now called ''[[Midy's Theorem]]'', in 1836. The publication was obscure, and it is unclear if his proof directly involved 0.999…, but at least one modern proof by W. G. Leavitt does. If one can prove that a decimal of the form 0.''b''1''b''2''b''3… is a positive integer, then it must be 0.999…, which is then the source of the 9s in the theorem.<ref>Leavitt 1984 p.301</ref> Investigations in this direction can motivate such concepts as [[greatest common divisor]]s, [[modular arithmetic]], [[Fermat prime]]s, [[order (group theory)|order]] of [[group (mathematics)|group]] elements, and [[quadratic reciprocity]].<ref>Lewittes pp.1-3; Leavitt 1967 pp.669,673; Shrader-Frechette pp.96-98</ref>

[[Image:Cantor base 3.svg|right|thumb|Positions of 1/4, 2/3, and 1 in the Cantor set]]
Returning to real analysis, the base-3 analogue 0.222… = 1 plays a key role in a characterization of one of the simplest [[fractal]]s, the middle-thirds [[Cantor set]]:
*A point in the [[unit interval]] lies in the Cantor set if and only if it can be represented in ternary using only the digits 0 and 2.

The ''n''th digit of the representation reflects the position of the point in the ''n''th stage of the construction. For example, the point 2⁄3 is given the usual representation of 0.2 or 0.2000…, since it lies to the right of the first deletion and to the left of every deletion thereafter. The point 1⁄3 is represented not as 0.1 but as 0.0222…, since it lies to the left of the first deletion and to the right of every deletion thereafter.<ref>Pugh p.97; Alligood, Sauer, and Yorke pp.150-152. Protter and Morrey (p.507) and Pedrick (p.29) assign this description as an exercise.</ref>

Repeating nines also turn up in yet another of Georg Cantor's works. They must be taken into account to construct a valid proof, applying [[Cantor's diagonal argument|his 1891 diagonal argument]] to decimal expansions, of the [[uncountability]] of the unit interval. Such a proof needs to be able to declare certain pairs of real numbers to be different based on their decimal expansions, so one needs to avoid pairs like 0.2 and 0.1999… . A simple method represents all numbers with nonterminating expansions; the opposite method rules out repeating nines.<ref>Maor (p.60) and Mankiewicz (p.151) review the former method; Mankiewicz attributes it to Cantor, but the primary source is unclear. Munkres (p.50) mentions the latter method.</ref> A variant that may be closer to Cantor's original argument actually uses base 2, and by turning base-3 expansions into base-2 expansions, one can prove the uncountability of the Cantor set as well.<ref>Rudin p.50, Pugh p.98</ref>

== In popular culture ==

With the rise of the [[Internet]], debates about 0.999… have escaped the classroom and are commonplace on [[newsgroup]]s and [[message board]]s, including many that nominally have little to do with mathematics. In the newsgroup <tt>[[sci.math]]</tt>, arguing over 0.999… is a "popular sport", and it is one of the questions answered in its [[FAQ]].<ref>As observed by Richman (p.396). {{cite web |url=http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/ |author=Hans de Vreught | year=1994 | title=sci.math FAQ: Why is 0.9999… = 1? |accessdate=2006-06-29}}</ref> The FAQ briefly covers 1/3, multiplication by 10, and limits, and it alludes to Cauchy sequences as well.

A 2003 edition of the general-interest [[newspaper column]] ''[[The Straight Dope]]'' discusses 0.999… via 1/3 and limits, saying of misconceptions,
:"The lower primate in us still resists, saying: .999~ doesn't really represent a ''number'', then, but a ''process''. To find a number we have to halt the process, at which point the .999~ = 1 thing falls apart.

:Nonsense."<ref>{{cite web |url=http://www.straightdope.com/columns/030711.html |title=An infinite question: Why doesn't .999~ = 1? |date=2003-07-11 |author=[[Cecil Adams]] |work=[[The Straight Dope]] |publisher=[[The Chicago Reader]] |accessdate=2006-09-06}}</ref>

''The Straight Dope'' cites a discussion on its own message board that grew out of an unidentified "other message board ... mostly about video games". In the same vein, the question of 0.999… proved such a popular topic in the first seven years of [[Blizzard Entertainment]]'s [[Battle.net]] forums that the company's president, [[Mike Morhaime]], announced at an [[April 1]], 2004 [[press conference]] that it is 1:
:"We are very excited to close the book on this subject once and for all. We've witnessed the heartache and concern over whether .999~ does or does not equal 1, and we're proud that the following proof finally and conclusively addresses the issue for our customers."<ref>{{cite web |url=http://www.blizzard.com/press/040401.shtml |title=Blizzard Entertainment® Announces .999~ (Repeating) = 1 |work=Press Release |publisher=Blizzard Entertainment |date=2004-04-01 |accessdate=2006-09-03}}</ref>
Blizzard's subsequent [[press release]] offers two proofs, based on limits and multiplication by 10.

== Related questions ==


*[[Zeno's paradoxes]], particularly the runner paradox, are reminiscent of the apparent paradox that 0.999… and 1 are equal. The runner paradox can be mathematically modelled and then, like 0.999…, resolved using a geometric series. However, it is not clear if this mathematical treatment addresses the underlying metaphysical issues Zeno was after.<ref>Wallace p.51, Maor p.17</ref>
*[[Division by zero]] occurs in some popular discussions of 0.999…, and it also stirs up contention. While most authors choose to define 0.999…, almost all modern treatments leave division by zero undefined, as it can be given no meaning in the standard real numbers. In other systems, such as the [[Riemann sphere]], it makes sense to define 1/0 to be infinity.<ref>See, for example, J.B. Conway's treatment of Möbius transformations, pp.47-57</ref> In fact, some prominent mathematicians argued for such a definition long before either number system was developed.<ref>Maor p.54</ref>
*[[Negative zero]] is another redundant feature of many ways of writing numbers. In number systems, such as the real numbers, where "0" denotes the additive identity and is neither positive nor negative, the usual interpretation of "−0" is that it should denote the additive inverse of 0, which forces −0 = 0.<ref>Munkres p.34, Exercise 1(c)</ref> Nonetheless, some scientific applications use separate positive and negative zeroes, as do some of the most common computer number systems.<ref>{{cite book |author=Kroemer, Herbert; Kittel, Charles |title=Thermal Physics |edition=2e |publisher=W. H. Freeman |year=1980 |id=ISBN 0-7167-1088-9 |pages=462}}</ref><ref>{{cite web |url=http://msdn.microsoft.com/library/en-us/csspec/html/vclrfcsharpspec_4_1_6.asp |title=Floating point types |work=[[Microsoft Developer Network|MSDN]] C# Language Specification |accessdate=2006-08-29}}</ref>

==Notes==
<div class="references-2column">
<references />
</div>

==References==
<div class="references-small">
*{{cite book |author=Alligood, Sauer, and Yorke |year=1996 |title=Chaos: An introduction to dynamical systems |chapter=4.1 Cantor Sets |publisher=Springer |id=ISBN 0-387-94677-2}}
*:This introductory textbook on dynamics is aimed at undergraduate and beginning graduate students. (p.ix)
*{{cite book |last=Apostol |first=Tom M. |year=1974 |title=Mathematical analysis |edition=2e |publisher=Addison-Wesley |id=ISBN 0-201-00288-4}}
*:A transition from calculus to advanced analysis, ''Mathematical analysis'' is intended to be "honest, rigorous, up to date, and, at the same time, not too pedantic." (pref.) Apostol's development of the real numbers uses the least upper bound axiom and introduces infinite decimals two pages later. (pp.9-11)
*{{cite book |author=Bartle, R.G. and D.R. Sherbert |year=1982 |title=Introduction to real analysis |publisher=Wiley |id=ISBN 0-471-05944-7}}
*:This text aims to be "an accessible, reasonably paced textbook that deals with the fundamental concepts and techniques of real analysis." Its development of the real numbers relies on the supremum axiom. (pp.vii-viii)
*{{cite book |last=Beals |first=Richard |title=Analysis |year=2004 |publisher=Cambridge UP |id=ISBN 0-521-60047-2}}
*{{cite book |author=[[Elwyn Berlekamp|Berlekamp, E.R.]]; [[John Horton Conway|J.H. Conway]]; and [[Richard K. Guy|R.K. Guy]] |year=1982 |title=[[Winning Ways for your Mathematical Plays]] |publisher=Academic Press |id=ISBN 0-12-091101-9}}
*{{cite conference |last=Berz |first=Martin |title=Automatic differentiation as nonarchimedean analysis |year=1992 |booktitle=Computer Arithmetic and Enclosure Methods |publisher=Elsevier |pages=439-450 |url=http://citeseer.ist.psu.edu/berz92automatic.html}}
*{{cite book |last=Bunch |first=Bryan H. |title=Mathematical fallacies and paradoxes |year=1982 |publisher=Van Nostrand Reinhold |id=ISBN 0-442-24905-5}}
*:This book presents an analysis of paradoxes and fallacies as a tool for exploring its central topic, "the rather tenuous relationship between mathematical reality and physical reality". It assumes first-year high-school algebra; further mathematics is developed in the book, including geometric series in Chapter 2. Although 0.999... is not one of the paradoxes to be fully treated, it is briefly mentioned during a development of Cantor's diagonal method. (pp.ix-xi, 119)
*{{cite book |last=Burrell |first=Brian |title=Merriam-Webster's Guide to Everyday Math: A Home and Business Reference |year=1998 |publisher=Merriam-Webster |id=ISBN 0877796211}}
*{{cite book |last=Conway |first=John B. |authorlink=John B. Conway |title=Functions of one complex variable I |edition=2e |publisher=Springer-Verlag |origyear=1973 |year=1978 |id=ISBN 0-387-90328-3}}
*:This text assumes "a stiff course in basic calculus" as a prerequisite; its stated principles are to present complex analysis as "An Introduction to Mathematics" and to state the material clearly and precisely. (p.vii)
*{{cite book |last=Davies |first=Charles |year=1846 |title=The University Arithmetic: Embracing the Science of Numbers, and Their Numerous Applications |publisher=A.S. Barnes |url=http://books.google.com/books?vid=LCCN02026287&pg=PA175}}
*{{cite journal |last=DeSua |first=Frank C. |title=A system isomorphic to the reals |format=restricted access |journal=The American Mathematical Monthly |volume=67 |number=9 |month=November |year=1960 |pages=900-903 |url=http://links.jstor.org/sici?sici=0002-9890%28196011%2967%3A9%3C900%3AASITTR%3E2.0.CO%3B2-F}}
*{{cite journal |author=Dubinsky, Ed, Kirk Weller, Michael McDonald, and Anne Brown |title=Some historical issues and paradoxes regarding the concept of infinity: an APOS analysis: part 2 |journal=Educational Studies in Mathematics |year=2005 |volume=60 |pages=253-266 |id={{doi|10.1007/s10649-005-0473-0}}}}
*{{cite journal |author=Edwards, Barbara and Michael Ward |year=2004 |month=May |title=Surprises from mathematics education research: Student (mis)use of mathematical definitions |journal=The American Mathematical Monthly |volume=111 |number=5 |pages=411-425}}
*{{cite book |last=Enderton |first=Herbert B. |year=1977 |title=Elements of set theory |publisher=Elsevier |id=ISBN 0-12-238440-7}}
*:An introductory undergraduate textbook in set theory that "presupposes no specific background". It is written to accommodate a course focusing on axiomatic set theory or on the construction of number systems; the axiomatic material is marked such that it may be de-emphasized. (pp.xi-xii)
*{{cite book |last=Euler |first=Leonard |authorlink=Leonard Euler |origyear=1770 |year=1822 |edition=3rd English edition |title=Elements of Algebra |editor=John Hewlett and Francis Horner, English translators. |publisher=Orme Longman |url=http://books.google.com/books?id=X8yv0sj4_1YC&pg=PA170}}
*{{cite journal |last=Fjelstad |first=Paul |title=The repeating integer paradox |format=restricted access |journal=The College Mathematics Journal |volume=26 |number=1 |month=January |year=1995 |pages=11-15 |url=http://links.jstor.org/sici?sici=0746-8342%28199501%2926%3A1%3C11%3ATRIP%3E2.0.CO%3B2-X |id={{doi|10.2307/2687285}}}}
*{{cite book |last=Gardiner |first=Anthony |title=Understanding Infinity: The Mathematics of Infinite Processes |origyear=1982 |year=2003 |publisher=Dover |id=ISBN 0-486-42538-X}}
*{{cite book |last=Gowers |first=Timothy |title=Mathematics: A Very Short Introduction |year=2002 |publisher=Oxford UP |id=ISBN 0-19-285361-9}}
*{{cite book |last=Grattan-Guinness |first=Ivor |year=1970 |title=The development of the foundations of mathematical analysis from Euler to Riemann |publisher=MIT Press |id=ISBN 0-262-07034-0}}
*{{cite book | last=Griffiths | first=H.B. | coauthors=P.J. Hilton | title=A Comprehensive Textbook of Classical Mathematics: A Contemporary Interpretation | year=1970 | publisher=Van Nostrand Reinhold | location=London | id=ISBN 0-442-02863-6. {{LCC|QA37.2|G75}}}}
*:This book grew out of a course for [[Birmingham]]-area [[grammar school]] mathematics teachers. The course was intended to convey a university-level perspective on [[mathematics education|school mathematics]], and the book is aimed at students "who have reached roughly the level of completing one year of specialist mathematical study at a university". The real numbers are constructed in Chapter 24, "perhaps the most difficult chapter in the entire book", although the authors ascribe much of the difficulty to their use of [[ideal theory]], which is not reproduced here. (pp.vii, xiv)
*{{cite journal |last=Kempner |first=A.J. |title=Anormal Systems of Numeration |format=restricted access |journal=The American Mathematical Monthly |volume=43 |number=10 |month=December |year=1936 |pages=610-617 |url=http://links.jstor.org/sici?sici=0002-9890%28193612%2943%3A10%3C610%3AASON%3E2.0.CO%3B2-0}}
*{{cite journal |author=Komornik, Vilmos; and Paola Loreti |title=Unique Developments in Non-Integer Bases |format=restricted access |journal=The American Mathematical Monthly |volume=105 |number=7 |year=1998 |pages=636-639 |url=http://links.jstor.org/sici?sici=0002-9890%28199808%2F09%29105%3A7%3C636%3AUDINB%3E2.0.CO%3B2-G}}
*{{cite journal |last=Leavitt |first=W.G. |title=A Theorem on Repeating Decimals |format=restricted access |journal=The American Mathematical Monthly |volume=74 |number=6 |year=1967 |pages=669-673 |url=http://links.jstor.org/sici?sici=0002-9890%28196706%2F07%2974%3A6%3C669%3AATORD%3E2.0.CO%3B2-0}}
*{{cite journal |last=Leavitt |first=W.G. |title=Repeating Decimals |format=restricted access |journal=The College Mathematics Journal |volume=15 |number=4 |month=September |year=1984 |pages=299-308 |url=http://links.jstor.org/sici?sici=0746-8342%28198409%2915%3A4%3C299%3ARD%3E2.0.CO%3B2-D}}
*{{cite web | url=http://arxiv.org/abs/math.NT/0605182 |title=Midy's Theorem for Periodic Decimals |last=Lewittes |first=Joseph |work=New York Number Theory Workshop on Combinatorial and Additive Number Theory |year=2006 |publisher=[[arXiv]]}}
*{{cite journal |last=Lightstone |first=A.H. |title=Infinitesimals |format=restricted access |journal=The American Mathematical Monthly |year=1972 |volume=79 |number=3 |month=March |pages=242-251 |url=http://links.jstor.org/sici?sici=0002-9890%28197203%2979%3A3%3C242%3AI%3E2.0.CO%3B2-F}}
*{{cite book |last=Mankiewicz |first=Richard |year=2000 |title=The story of mathematics|publisher=Cassell |id=ISBN 0-304-35473-2}}
*:Mankiewicz seeks to represent "the history of mathematics in an accessible style" by combining visual and qualitative aspects of mathematics, mathematicians' writings, and historical sketches. (p.8)
*{{cite book |last=Maor |first=Eli |title=To infinity and beyond: a cultural history of the infinite |year=1987 |publisher=Birkhäuser |id=ISBN 3-7643-3325-1}}
*:A topical rather than chronological review of infinity, this book is "intended for the general reader" but "told from the point of view of a mathematician". On the dilemma of rigor versus readable language, Maor comments, "I hope I have succeeded in properly addressing this problem." (pp.x-xiii)
*{{cite book |last=Mazur |first=Joseph |title=Euclid in the Rainforest: Discovering Universal Truths in Logic and Math |year=2005 |publisher=Pearson: Pi Press |id=ISBN 0-13-147994-6}}
*{{cite book |last=Munkres |first=James R. |title=Topology |year=2000 |origyear=1975 |edition=2e |publisher=Prentice-Hall |id=ISBN 0-13-181629-2}}
*:Intended as an introduction "at the senior or first-year graduate level" with no formal prerequisites: "I do not even assume the reader knows much set theory." (p.xi) Munkres' treatment of the reals is axiomatic; he claims of bare-hands constructions, "This way of approaching the subject takes a good deal of time and effort and is of greater logical than mathematical interest." (p.30)
*{{cite book |last=Pedrick |first=George |title=A First Course in Analysis |year=1994 |publisher=Springer |id=ISBN 0-387-94108-8}}
*{{cite journal |last=Petkovšek |first=Marko |title=Ambiguous Numbers are Dense |format=restricted access |journal=[[The American Mathematical Monthly|American Mathematical Monthly]] |volume=97 |number=5 |month=May |year=1990 |pages=408-411 |url=http://links.jstor.org/sici?sici=0002-9890%28199005%2997%3A5%3C408%3AANAD%3E2.0.CO%3B2-Q}}
*{{cite conference |author=Pinto, Márcia and David Tall |title=Following students' development in a traditional university analysis course |booktitle=PME25 |pages=v4: 57-64 |year=2001 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001j-pme25-pinto-tall.pdf}}
*{{cite book |author=Protter, M.H. and C.B. Morrey |year=1991 |edition=2e |title=A first course in real analysis |publisher=Springer |id=ISBN 0-387-97437-7}}
*:This book aims to "present a theoretical foundation of analysis that is suitable for students who have completed a standard course in calculus." (p.vii) At the end of Chapter 2, the authors assume as an axiom for the real numbers that bounded, nodecreasing sequences converge, later proving the nested intervals theorem and the least upper bound property. (pp.56-64) Decimal expansions appear in Appendix 3, "Expansions of real numbers in any base". (pp.503-507)
*{{cite book |last=Pugh |first=Charles Chapman |title=Real mathematical analysis |year=2001 |publisher=Springer-Verlag |id=ISBN 0-387-95297-7}}
*:While assuming familiarity with the rational numbers, Pugh introduces Dedekind cuts as soon as possible, saying of the axiomatic treatment, "This is something of a fraud, considering that the entire structure of analysis is built on the real number system." (p.10) After proving the least upper bound property and some allied facts, cuts are not used in the rest of the book.
*{{cite journal |first=Fred |last=Richman |year=1999 |month=December |title=Is 0.999… = 1? |format=restricted access |journal=[[Mathematics Magazine]] |volume=72 |issue=5 |pages=396-400 |url=http://links.jstor.org/sici?sici=0025-570X%28199912%2972%3A5%3C396%3AI0.%3D1%3E2.0.CO%3B2-F}} Free HTML preprint: {{cite web |url=http://www.math.fau.edu/Richman/HTML/999.htm |first=Fred|last=Richman|title=Is 0.999… = 1? |date=1999-06-08 |accessdate=2006-08-23}} Note: the journal article contains material and wording not found in the preprint.
*{{cite book |last=Robinson |first=Abraham |authorlink=Abraham Robinson |title=Non-standard analysis |year=1996 |edition=Revised edition |publisher=Princeton University Press|id=ISBN 0-691-04490-2}}
*{{cite book |last=Rosenlicht |first=Maxwell |year=1985 |title=Introduction to Analysis |publisher=Dover |id=ISBN 0-486-65038-3}}
*{{cite book |last=Rudin |first=Walter |authorlink=Walter Rudin |title=Principles of mathematical analysis |edition=3e |year=1976 |origyear=1953 |publisher=McGraw-Hill |id=ISBN 0-07-054235-X}}
*:A textbook for an advanced undergraduate course. "Experience has convinced me that it is pedagogically unsound (though logically correct) to start off with the construction of the real numbers from the rational ones. At the beginning, most students simply fail to appreciate the need for doing this. Accordingly, the real number system is introduced as an ordered field with the least-upper-bound property, and a few interesting applications of this property are quickly made. However, Dedekind's construction is not omitted. It is now in an Appendix to Chapter 1, where it may be studied and enjoyed whenever the time is ripe." (p.ix)
*{{cite journal |last=Shrader-Frechette |first=Maurice |title=Complementary Rational Numbers |format=restricted access |journal=Mathematics Magazine |volume=51 |number=2 |month=March |year=1978 |pages=90-98 |url=http://links.jstor.org/sici?sici=0025-570X%28197803%2951%3A2%3C90%3ACRN%3E2.0.CO%3B2-O}}
*{{cite book |author=Smith, Charles and Charles Harrington |year=1895 |title=Arithmetic for Schools |publisher=Macmillan |url=http://books.google.com/books?vid=LCCN02029670&pg=PA115}}
*{{cite book |last=Sohrab |first=Houshang |title=Basic Real Analysis |year=2003 |publisher=Birkhäuser |id=ISBN 0-8176-4211-0}}
*{{cite book |last=Stewart |first=Ian |title=The Foundations of Mathematics |year=1977 |publisher=Oxford UP |id=ISBN 0-19-853165-6}}
*{{cite book |last=Stewart |first=James |title=Calculus: Early transcendentals |edition=4e |year=1999 |publisher=Brooks/Cole |id=ISBN 0-534-36298-2}}
*:This book aims to "assist students in discovering calculus" and "to foster conceptual understanding". (p.v) It omits proofs of the foundations of calculus.
*{{cite journal |author=D.O. Tall and R.L.E. Schwarzenberger |title=Conflicts in the Learning of Real Numbers and Limits |journal=Mathematics Teaching |year=1978 |volume=82 |pages=44-49 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1978c-with-rolph.pdf}}
*{{cite journal |last=Tall |first=David |authorlink=David Tall |title=Conflicts and Catastrophes in the Learning of Mathematics |journal=Mathematical Education for Teaching |year=1976/7 |volume=2 |number=4 |pages=2-18 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1976a-confl-catastrophy.pdf}}
*{{cite journal |last=Tall |first=David |title=Cognitive Development In Advanced Mathematics Using Technology |journal=Mathematics Education Research Journal |year=2000 |volume=12 |number=3 |pages=210-230 |url=http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001b-merj-amt.pdf}}
*{{cite book|last=von Mangoldt|first=Dr. Hans|authorlink =Hans Carl Friedrich von Mangoldt| title=Einführung in die höhere Mathematik|edition=1st ed.|year=1911|publisher=Verlag von S. Hirzel| location=Leipzig|language=German|chapter=Reihenzahlen}}
*{{cite book |last=Wallace |first=David Foster |title=Everything and more: a compact history of infinity |year=2003 |publisher=Norton |id=ISBN 0-393-00338-8}}
</div>

== External links==
{{commons|0.999...}}
*[http://www.cut-the-knot.org/arithmetic/999999.shtml .999999... = 1?] from [[cut-the-knot]]
*[http://mathforum.org/dr.math/faq/faq.0.9999.html Why does 0.9999… = 1 ?]
*[http://www.newton.dep.anl.gov/askasci/math99/math99167.htm Ask A Scientist: Repeating Decimals]
*[http://descmath.com/diag/nines.html Repeating Nines]
*[http://qntm.org/pointnine Point nine recurring equals one]
*[http://www.warwick.ac.uk/staff/David.Tall/themes/limits-infinity.html David Tall's research on mathematics cognition]

{{featured article}}

[[Category:Mathematics paradoxes]]
[[Category:Real analysis]]
[[Category:Real numbers]]
[[Category:Numeration]]
[[Category:Proofs]]

[[es:0,9 periódico]]
[[fr:Développement décimal de l'unité]]
[[ja:0.999...が1に等しいことの証明]]
[[th:การพิสูจน์ว่า 0.999... เท่ากับ 1]]
[[zh:证明0.999...等于1]]

Drop Bear

2006-08-17T01:18:32Z

Simetrical: Standardize hatnote

{{otheruses4|the Dropbear open source SSH server and client project|Dropbear}}
A '''drop bear''' (or '''dropbear''') is a fictitious [[Australia]]n [[marsupial]] supposedly related to the [[koala]].

Drop bears are commonly said to be unusually large, vicious, [[carnivorous]] koalas that inhabit treetops and attack their prey by dropping onto their heads from above. They are an example of local lore intended to frighten and confuse outsiders, and amuse locals, similar to the [[jackalope]], [[hoop snake]] or [[haggis]] hunting.

Some suggest that the drop bear myth is designed to discourage children from straying needlessly below [[eucalyptus]] trees, protecting them from the very real danger of getting hit by a falling branch. Arbitrary detachment of old branches is common with certain species of the [[Eucalyptus|eucalyptus]], which are known as 'widow-makers' for this very reason.

The drop bear myth appears to have first appeared during the latter half of the [[20th century]], and may have its origins with the ''[[Phascolarctos stirtoni]]'', the carnivorous ''[[Phascolarctos involus]]'' or perhaps the ''[[Thylacoleo carnifex]]'', which belong to a group of [[extinct]] animals known as [[Australian megafauna]]. The prehistoric creatures were approximately twice the size of modern koalas. The thylacoleo is thought to have been an arboreal predator that may well have ambushed prey by dropping on it from overhead branches.

Stories of drop bears are often told to unsuspecting foreign visitors to illustrate Australian [[deadpan]] humour. It is suggested that doing ridiculous things like having forks in the hair or [[Vegemite]] or toothpaste spread behind the ears will deter the creatures. Such precautions are lent credibility by the fact that [[Australian Magpie|Australian Magpies]] can be [[Australian_Magpie#Swooping|deterred from attacking]] by wearing sunglasses on the back of the head.

==Drop bears in popular culture==

*Dropbears appear in the novel ''[[The Last Continent]]'' by [[Terry Pratchett]]. In that novel, the wizard [[Rincewind]] travels through the continent of [[FourEcks]], and is attacked by some of the creatures while traveling through the desert. Rincewind is wearing the traditional pointed wizard's hat, which impales the creature.
*The Dropbears was a [[Sydney]], [[Australia]] band from [[1981]] until [[1985]], with members Johnny Bachelor, Chriss Cross, Jamie Elliot, Phil Hall, Robert Hearne, Michael Knapp and Simon Rudin. They had a minor charting hit with ''Shall We Go'' in 1985. [http://rateyourmusic.com/release/album/dropbears/dropbears/]
*Drop bears appear in the game "[[Escape Velocity Nova|Escape Velocity: Nova]]." The game's drop bears are actually human (specifically, Auroran) pranksters in disguise. "Drop bear repellant" may be purchased, but this will only single out the player as a gullible customer, and increase the frequency of drop bear attacks.
*Drop Bears have also appeared in the [[webcomics]] [[Indie Tits]] (November 7-14, 2005) and [[User Friendly]].
*[[dropbear]] is a SSH 2 server and client that is designed to be small enough to be used in low-memory embedded environments, while still being functional and secure enough for general use.
*A 2004 commercial for [[Bundaberg Rum]] showed three Scandinavian women camping under a tree, when four Australian men stated that they shouldn't camp there as there were "drop bears - a bigger meaner koala" and that "they grab your head". Laughing this off they return to setting up camp when "Bundy Bear", the seven-foot tall polar bear mascot for Bundaberg Rum, falls from the tree above. The girls then run in fear into the Australian men's camp.
*The [[Shadowrun]] supplement 'Target: Awakened Lands' lists Drop Bears as being Koalas infected with a virus similar to that which causes vampirism in humans.
*The [[d20 Modern]] Menace Manual has a Drop Bear listed.
*An episode of [[The Paul Hogan Show]] in [[1981]] featured killer koalas in a sendup of [[Raiders of the Lost Ark]] called Wreckers of the Lost Park. These killer koalas would drop out of trees and attack people.
*The [[Nextwave]] team is bombed with Drop Bears over several pages of Nextwave #5.
[[Category:In-jokes|*]]

== See also ==
* [[Fictional national animals]]
* [[Hoop snake]]
* [[Bunyip]]
* [[Yowie (cryptid)|Yowie]]
* [[Jackalope]]
* [[Pacific Northwest Tree Octopus]]
* [[Queensland Tiger]]

==External links==
* [http://geocities.com/muirnin/db.htm Drop Bears - The Truth] - A humorous website describing various imaginary species of dropbear.

[[Category:In-jokes]]
[[Category:Fictional species]]
[[Category:Folklore of Australia]]
[[Category:Legendary creatures]]
[[Category:Australian culture]]
[[pl:Drop bear]]

Physik in Animationsfilmen

2006-06-09T06:53:51Z

Simetrical: /* Cartoon collision physics */ Numbered list

'''Cartoon physics''' is a joking reference to the fact that [[animation]] allows regular [[law of physics|laws of physics]] to be ignored in [[humor|humorous]] ways. For example, when a cartoon character runs off a cliff, [[gravity]] has no effect until the character notices and mugs an appropriate reaction.<ref name="coyotusinterruptus">In a [[neologism]] contest held by ''[[New Scientist]]'', a winning entry coined the term "coyotus interruptus" for this phenomenon—a pun on [[coitus interruptus]] and [[Wile E. Coyote]], who fell to his doom this way particularly often.</ref>

The phrase also reflects the fact that many of the most famous [[United States|American]] [[animated cartoon]]s, particularly those from [[Warner Brothers]] and [[MGM]] studios, unconsciously developed a relatively consistent set of such "laws" that have become regularly applied in comic animation.

The idea that cartoons behave differently, but not randomly, than the real world is virtually as old as animation. [[Walt Disney]], for example, spoke of the ''plausible impossible'' (see [[The Plausible Impossible]], 1956), deliberately mispronouncing the second word so it rhymed with the first.

Specific reference to cartoon physics extends back at least to June of [[1980]], when an article "O'Donnell's Laws of Cartoon Motion"<ref>O'Donnell's Laws of Cartoon Motion", ''Esquire'', 6/80, reprinted in ''IEEE Institute'', 10/94; V.18 #7 p.12. [http://remarque.org/~doug/cartoon-physics.html Copy on Web]</ref> appeared in ''[[Esquire magazine]]''. A version printed in [[1994]] by the [[IEEE]] in a journal for [[engineering|engineers]] helped spread the word among the technical crowd, which has expanded and refined the idea. Dozens of websites exist outlining these laws.

The situation is so well-understood that it has been used as the topic of jokes for decades, as in the 1949 [[Looney Tunes]] short ''[[High Diving Hare]]'', in which [[Bugs Bunny]] explains, "I know this defies the law of gravity; but you see, I haven't studied law!"

More recently, the cartoon characters [[Roger Rabbit]] and [[Bonkers (TV series)|Bonkers D. Bobcat]] have their own variations on the theme, explaining that [[toon]]s are allowed to bend or break natural laws for the purposes of comedy. Doing this is extremely tricky, so [[toon]]s have a natural sense of comedic timing, giving them inherently funny properties. Bonkers also warns that the loss of this sense can lead to unfunny and even dangerous situations, perhaps explaining why cartoon violence, but not the real variety, is always funny.

In 1993, [[Stephen J. Gould]] writing in ''[[New Scientist]]'' noted that "... new, looney toon analysis reveals that these, seemingly nonsensical, phenomena can be described by logical laws similar to those in our world. Nonsensical events are by no means limited to the Looniverse. Laws that govern our own Universe often seem contrary to common sense."<ref>Stephen J. Gould, [http://www.newscientist.com/article/mg14019055.200.html Looney Tuniverse: There is a crazy kind of physics at work in the world of cartoons] (1993) ''New Scientist''</ref>. This theme is further described by Dr. Alan Cholodenko in his article, "The Nutty Universe of Animation" <ref>Dr. Alan Cholodenko, "[http://www.ubishops.ca/baudrillardstudies/vol3_1/cholodenkopf.htm The Nutty Universe of Animation, The “Discipline” of All “Disciplines”, And That’s Not All, Folks!]" ''International Journal of Baudrillard Studies'' Volume 3, Number 1 (January 2006)</ref>

== Why is it funny? ==

Adherents of [[evolutionary psychology]] have suggested that the humorous effect of cartoon physics is due to the interplay of intuitions between [[physics]] (objective) and [[psychology]] (self-perception). The physics module predicts that the cartoon character will fall over the cliff immediately, while the psychology module anthropomorphizes the force of gravity and thus see it as vulnerable to deception, as long as the actor is self-deceived {{cite needed}}.

In short, it can lead to the humorous situation where a cartoon's logic is governed by what "makes sense" (is consistent) rather than what "is" (natural law).

== Examples ==
Commonly cited cartoon physics "laws" include:

* No matter what happens to [[cat]]s, they always return to their default shapes.
* Any body passing through solid matter will leave a dent or cutout conforming to its perimeter. (This is obviously not true in real life; a flimsier body will break and leave a different-shaped hole. Compare to the [[9/11 conspiracy theories|conspiracy theories regarding]] the fate of [[American Airlines Flight 77]], which left a hole in the Pentagon not conforming to its perimeter.)
* [[Explosive material|Explosives]], even if detonated close to a character's face, will cause only scorching of the skin. (Prior to the efforts of the [[American Civil Rights Movement]], characters would often take on the appearance of [[blackface]].) Similarly, a gun discharged directly into the face will not fire an actual bullet.
* If a character walks off a cliff, they will not fall, and continue to walk on thin air, until they notice they have walked off the cliff. In some cases a character can avoid falling, even if they are aware there is no ground below them.
* Alternatively, when a character runs off a cliff, notices the situation, and begins falling, at first only the body below the neck falls, during which the neck is stretched for a few seconds before the head follows.
* If a character falls from a tall building, another character from the same floor will be able to run all the way down to ground level in order to catch the falling character before he/she hits the ground.
* Characters are allowed to "swim" or blow themselves upwards a short distance in the air before falling normally to gravity.
* When a character chops the only thing holding another character from falling (such as a tree branch) the chopper will fall, together with whatever he/she was standing on (such as the tree or the ground) and the other character will remain floating in the air (branch included).
* An explosive device taken by one character will not explode until it is given back to the original character who triggered the device. Also applies to [[booby traps]].
* A [[boomerang]], when thrown, will not only change direction, but will actively hunt out its thrower so that the thrower may catch it (or be hit by it), regardless of his or her relation to the initial point of the throw.
* Motion reference frames are arbitrary. For instance, an outboard motor in a pan of water on wheels causes the motor and pan to move together. Likewise, a fan and a sail attached to a wheeled platform will cause the platform to move.
* A gun may be fired any number of times without being reloaded.
* Any fall is survivable.
* [[Cartoon hole|Holes]] can be physically picked up and moved. This also applies to mouths.

== Anvilology ==
'''Anvilology'''{{fact}} is the study of (cartoon) physical principles of [[anvil]]s, as studied at "Acme Looniversity" in the animated series, ''[[Tiny Toons]]''.
* Everything falls faster than an anvil (so that the evil character can hit the ground first and then be crushed, but not killed, by the anvil).
* Anvils are readily available.
* Anvils have [[mass]] but not much [[weight]], so that they are very hard to push around, but it is possible to jump out of a plane with an anvil instead of a parachute and not notice until the parachute is opened while airborne.
* Anvils can stay in the air until noticed by a character, at which point they fall on the character.
* If a character moves out of the way of a falling anvil, the anvil will shift its position over the character before falling, so that it crushes (but does not kill) the character.

== Cartoon collision physics ==

'''Cartoon collision physics''' are a subset of cartoon physics regarding the laws of collisions. Note that these laws deliberately refer to male subjects; bad things do not generally happen to women.

For a given cartoon character C:
#If C runs into a wall,
#:a: If the wall is too thick, C will strike it and flatten out like [[dough]], often regardless of clothing.
#:b: If the wall is thin enough, he will leave a hole in the wall in the shape of his body.
#If C runs into something made of metal, he will dent it in the shape of his body.
#If C runs off a cliff, the [[impact crater]] he leaves will conform with Rule 1b.
#If C has a fragile body,
#:a: Running into any wall will cause him to be squashed into a [[musical instrument]] (usually an [[accordion]]), or
#:b: Any collision or fall will fracture him into a [[zillion]] pieces.
#If C runs into a wall which has been painted to look like part of the landscape or a tunnel:
#:a: If the "camera" angle blends the painting with the actual landscape, he will enter the landscape or tunnel as though it were real.
#:b: If he was the one who painted the wall, he will just run into the wall — see Rule 1.
#:c: If the "camera" views the painting at an angle such that it is, without doubt, a painting on a wall, he will just run into the wall — see Rule 1.
#:d: Trains or large trucks are often known to drive out of walls painted in this way, usually just after the painter has slammed into the wall and is feeling sheepish for having fallen for their own ruse. However, if the view of the oncoming vehicle is blocked, then the vehicle will apparently stop.

== Laws of Cartoon Thermodynamics ==

The Laws of Cartoon Thermodynamics are physical laws in the [[Animation|cartoon]] universe identified by [[Trevor Paquette]] and Lt. [[Justin D. Baldwin]] and popularized by film critic [[Roger Ebert]]. They overlap greatly with the older concept of "laws of [[cartoon physics]]".

*Any body suspended in space will remain in space until made aware of its situation (plus an interval for live falling bodies to express an appropriate emotion).
*Any body in motion will tend to remain in motion until solid matter intervenes suddenly.
*Any body passing through solid matter will leave a perforation conforming to its perimeter.
*The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken.
*All principles of gravity are negated by fear.
*As speed increases, objects can be in several places at once.
*Certain bodies can pass through solid walls painted to resemble tunnel entrances; others cannot.
*Any violent rearrangement of feline matter is impermanent.
*Everything falls faster than an anvil.
*Guns, no matter how powerful, or no matter where aimed, will do nothing more than char flesh, blow away feathers, or rearrange beaks. In certain ocasions, they leave a perfectly circular hole that goes completely through the body of the character being shot, but this does not affect his/her health in any way.
*Any given amount of explosives will propel a body miles away, but still in one piece, charred and extremely peeved.
* Arms holding large falling weights are infinitely elastic, but will eventually drag the holder along.

== Anime physics ==

[[Anime]] physics can be considered a subset of cartoon physics - a set of rules used in cartoons to twist or ignore the laws of physics for humorous or dramatic effect. These are commonly seen in anime but not so common in cartoons. Normally, these are referenced from popular series in the past.
Note that many of these laws only apply to [[shounen]] series.

Examples include:

*Dramatic moments tend to distort time, either by slowing it down (usually long enough to call out the name of an attacker or the name of the "special move" used in the attack, or for bystanders to comment on the situation), or by looping three times.
**Similarly, transformations (especially those animated with [[stock footage]]) also seem to stop time until completed, allowing them to be used to counter attacks, or not allowing the person to be attacked while performing them.

*An angry or embarrassed girl will be able to hit any male (usually one who is romantically involved with her) hard enough to knock him into [[low Earth orbit]] and the male will usually survive.

*Attacks strong enough to shred entire planets will not destroy anyone's pants (but will usually destroy all other clothing). Conversely, certain explosions can destroy a female character's clothing without significantly harming her body—in some cases, without her initially noticing this.

*Any fire-based attack on a character will not completely burn his/her clothes but will leave black stains instead.

== Notes ==
<references />

== External links ==
*[http://funnies.paco.to/cartoon.html Cartoon Laws of Physics]
*[http://www.cs.utah.edu/~duongsaa/more_htm/jk_100animeRules.htm 100 Laws of Anime Physics]
*[http://www.animeinfo.org/animeu/phys101.html Animeinfo.org: Anime Physics]
*[http://www.abcb.com/laws The Laws of Anime]
*[http://rogerebert.suntimes.com/apps/pbcs.dll/article?AID=/20050210/GLOSSARY/50213001/1005 Laws of Cartoon Thermodynamics] from [[Roger Ebert]]'s website.

[[Category:Cartoon physics|*]]

[[ja:マンガ物理学]]
[[zh:动画物理学]]

Physik in Animationsfilmen

2006-06-09T06:51:48Z

Simetrical: /* Examples */ Compare to the Pentagon attack

'''Cartoon physics''' is a joking reference to the fact that [[animation]] allows regular [[law of physics|laws of physics]] to be ignored in [[humor|humorous]] ways. For example, when a cartoon character runs off a cliff, [[gravity]] has no effect until the character notices and mugs an appropriate reaction.<ref name="coyotusinterruptus">In a [[neologism]] contest held by ''[[New Scientist]]'', a winning entry coined the term "coyotus interruptus" for this phenomenon—a pun on [[coitus interruptus]] and [[Wile E. Coyote]], who fell to his doom this way particularly often.</ref>

The phrase also reflects the fact that many of the most famous [[United States|American]] [[animated cartoon]]s, particularly those from [[Warner Brothers]] and [[MGM]] studios, unconsciously developed a relatively consistent set of such "laws" that have become regularly applied in comic animation.

The idea that cartoons behave differently, but not randomly, than the real world is virtually as old as animation. [[Walt Disney]], for example, spoke of the ''plausible impossible'' (see [[The Plausible Impossible]], 1956), deliberately mispronouncing the second word so it rhymed with the first.

Specific reference to cartoon physics extends back at least to June of [[1980]], when an article "O'Donnell's Laws of Cartoon Motion"<ref>O'Donnell's Laws of Cartoon Motion", ''Esquire'', 6/80, reprinted in ''IEEE Institute'', 10/94; V.18 #7 p.12. [http://remarque.org/~doug/cartoon-physics.html Copy on Web]</ref> appeared in ''[[Esquire magazine]]''. A version printed in [[1994]] by the [[IEEE]] in a journal for [[engineering|engineers]] helped spread the word among the technical crowd, which has expanded and refined the idea. Dozens of websites exist outlining these laws.

The situation is so well-understood that it has been used as the topic of jokes for decades, as in the 1949 [[Looney Tunes]] short ''[[High Diving Hare]]'', in which [[Bugs Bunny]] explains, "I know this defies the law of gravity; but you see, I haven't studied law!"

More recently, the cartoon characters [[Roger Rabbit]] and [[Bonkers (TV series)|Bonkers D. Bobcat]] have their own variations on the theme, explaining that [[toon]]s are allowed to bend or break natural laws for the purposes of comedy. Doing this is extremely tricky, so [[toon]]s have a natural sense of comedic timing, giving them inherently funny properties. Bonkers also warns that the loss of this sense can lead to unfunny and even dangerous situations, perhaps explaining why cartoon violence, but not the real variety, is always funny.

In 1993, [[Stephen J. Gould]] writing in ''[[New Scientist]]'' noted that "... new, looney toon analysis reveals that these, seemingly nonsensical, phenomena can be described by logical laws similar to those in our world. Nonsensical events are by no means limited to the Looniverse. Laws that govern our own Universe often seem contrary to common sense."<ref>Stephen J. Gould, [http://www.newscientist.com/article/mg14019055.200.html Looney Tuniverse: There is a crazy kind of physics at work in the world of cartoons] (1993) ''New Scientist''</ref>. This theme is further described by Dr. Alan Cholodenko in his article, "The Nutty Universe of Animation" <ref>Dr. Alan Cholodenko, "[http://www.ubishops.ca/baudrillardstudies/vol3_1/cholodenkopf.htm The Nutty Universe of Animation, The “Discipline” of All “Disciplines”, And That’s Not All, Folks!]" ''International Journal of Baudrillard Studies'' Volume 3, Number 1 (January 2006)</ref>

== Why is it funny? ==

Adherents of [[evolutionary psychology]] have suggested that the humorous effect of cartoon physics is due to the interplay of intuitions between [[physics]] (objective) and [[psychology]] (self-perception). The physics module predicts that the cartoon character will fall over the cliff immediately, while the psychology module anthropomorphizes the force of gravity and thus see it as vulnerable to deception, as long as the actor is self-deceived {{cite needed}}.

In short, it can lead to the humorous situation where a cartoon's logic is governed by what "makes sense" (is consistent) rather than what "is" (natural law).

== Examples ==
Commonly cited cartoon physics "laws" include:

* No matter what happens to [[cat]]s, they always return to their default shapes.
* Any body passing through solid matter will leave a dent or cutout conforming to its perimeter. (This is obviously not true in real life; a flimsier body will break and leave a different-shaped hole. Compare to the [[9/11 conspiracy theories|conspiracy theories regarding]] the fate of [[American Airlines Flight 77]], which left a hole in the Pentagon not conforming to its perimeter.)
* [[Explosive material|Explosives]], even if detonated close to a character's face, will cause only scorching of the skin. (Prior to the efforts of the [[American Civil Rights Movement]], characters would often take on the appearance of [[blackface]].) Similarly, a gun discharged directly into the face will not fire an actual bullet.
* If a character walks off a cliff, they will not fall, and continue to walk on thin air, until they notice they have walked off the cliff. In some cases a character can avoid falling, even if they are aware there is no ground below them.
* Alternatively, when a character runs off a cliff, notices the situation, and begins falling, at first only the body below the neck falls, during which the neck is stretched for a few seconds before the head follows.
* If a character falls from a tall building, another character from the same floor will be able to run all the way down to ground level in order to catch the falling character before he/she hits the ground.
* Characters are allowed to "swim" or blow themselves upwards a short distance in the air before falling normally to gravity.
* When a character chops the only thing holding another character from falling (such as a tree branch) the chopper will fall, together with whatever he/she was standing on (such as the tree or the ground) and the other character will remain floating in the air (branch included).
* An explosive device taken by one character will not explode until it is given back to the original character who triggered the device. Also applies to [[booby traps]].
* A [[boomerang]], when thrown, will not only change direction, but will actively hunt out its thrower so that the thrower may catch it (or be hit by it), regardless of his or her relation to the initial point of the throw.
* Motion reference frames are arbitrary. For instance, an outboard motor in a pan of water on wheels causes the motor and pan to move together. Likewise, a fan and a sail attached to a wheeled platform will cause the platform to move.
* A gun may be fired any number of times without being reloaded.
* Any fall is survivable.
* [[Cartoon hole|Holes]] can be physically picked up and moved. This also applies to mouths.

== Anvilology ==
'''Anvilology'''{{fact}} is the study of (cartoon) physical principles of [[anvil]]s, as studied at "Acme Looniversity" in the animated series, ''[[Tiny Toons]]''.
* Everything falls faster than an anvil (so that the evil character can hit the ground first and then be crushed, but not killed, by the anvil).
* Anvils are readily available.
* Anvils have [[mass]] but not much [[weight]], so that they are very hard to push around, but it is possible to jump out of a plane with an anvil instead of a parachute and not notice until the parachute is opened while airborne.
* Anvils can stay in the air until noticed by a character, at which point they fall on the character.
* If a character moves out of the way of a falling anvil, the anvil will shift its position over the character before falling, so that it crushes (but does not kill) the character.

== Cartoon collision physics ==

'''Cartoon collision physics''' are a subset of cartoon physics regarding the laws of collisions. Note that these laws deliberately refer to male subjects; bad things do not generally happen to women.

For a given cartoon character C:
* 1. If C runs into a wall,
:a: If the wall is too thick, C will strike it and flatten out like [[dough]], often regardless of clothing.
:b: If the wall is thin enough, he will leave a hole in the wall in the shape of his body.
* 2. If C runs into something made of metal, he will dent it in the shape of his body.
* 3. If C runs off a cliff, the [[impact crater]] he leaves will conform with Rule 1b.
* 4. If C has a fragile body,
:a: Running into any wall will cause him to be squashed into a [[musical instrument]] (usually an [[accordion]]), or
:b: Any collision or fall will fracture him into a [[zillion]] pieces.
* 5. If C runs into a wall which has been painted to look like part of the landscape or a tunnel:
:a: If the "camera" angle blends the painting with the actual landscape, he will enter the landscape or tunnel as though it were real.
:b: If he was the one who painted the wall, he will just run into the wall — see Rule 1.
:c: If the "camera" views the painting at an angle such that it is, without doubt, a painting on a wall, he will just run into the wall — see Rule 1.
:d: Trains or large trucks are often known to drive out of walls painted in this way, usually just after the painter has slammed into the wall and is feeling sheepish for having fallen for their own ruse. However, if the view of the oncoming vehicle is blocked, then the vehicle will apparently stop.

== Laws of Cartoon Thermodynamics ==

The Laws of Cartoon Thermodynamics are physical laws in the [[Animation|cartoon]] universe identified by [[Trevor Paquette]] and Lt. [[Justin D. Baldwin]] and popularized by film critic [[Roger Ebert]]. They overlap greatly with the older concept of "laws of [[cartoon physics]]".

*Any body suspended in space will remain in space until made aware of its situation (plus an interval for live falling bodies to express an appropriate emotion).
*Any body in motion will tend to remain in motion until solid matter intervenes suddenly.
*Any body passing through solid matter will leave a perforation conforming to its perimeter.
*The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken.
*All principles of gravity are negated by fear.
*As speed increases, objects can be in several places at once.
*Certain bodies can pass through solid walls painted to resemble tunnel entrances; others cannot.
*Any violent rearrangement of feline matter is impermanent.
*Everything falls faster than an anvil.
*Guns, no matter how powerful, or no matter where aimed, will do nothing more than char flesh, blow away feathers, or rearrange beaks. In certain ocasions, they leave a perfectly circular hole that goes completely through the body of the character being shot, but this does not affect his/her health in any way.
*Any given amount of explosives will propel a body miles away, but still in one piece, charred and extremely peeved.
* Arms holding large falling weights are infinitely elastic, but will eventually drag the holder along.

== Anime physics ==

[[Anime]] physics can be considered a subset of cartoon physics - a set of rules used in cartoons to twist or ignore the laws of physics for humorous or dramatic effect. These are commonly seen in anime but not so common in cartoons. Normally, these are referenced from popular series in the past.
Note that many of these laws only apply to [[shounen]] series.

Examples include:

*Dramatic moments tend to distort time, either by slowing it down (usually long enough to call out the name of an attacker or the name of the "special move" used in the attack, or for bystanders to comment on the situation), or by looping three times.
**Similarly, transformations (especially those animated with [[stock footage]]) also seem to stop time until completed, allowing them to be used to counter attacks, or not allowing the person to be attacked while performing them.

*An angry or embarrassed girl will be able to hit any male (usually one who is romantically involved with her) hard enough to knock him into [[low Earth orbit]] and the male will usually survive.

*Attacks strong enough to shred entire planets will not destroy anyone's pants (but will usually destroy all other clothing). Conversely, certain explosions can destroy a female character's clothing without significantly harming her body—in some cases, without her initially noticing this.

*Any fire-based attack on a character will not completely burn his/her clothes but will leave black stains instead.

== Notes ==
<references />

== External links ==
*[http://funnies.paco.to/cartoon.html Cartoon Laws of Physics]
*[http://www.cs.utah.edu/~duongsaa/more_htm/jk_100animeRules.htm 100 Laws of Anime Physics]
*[http://www.animeinfo.org/animeu/phys101.html Animeinfo.org: Anime Physics]
*[http://www.abcb.com/laws The Laws of Anime]
*[http://rogerebert.suntimes.com/apps/pbcs.dll/article?AID=/20050210/GLOSSARY/50213001/1005 Laws of Cartoon Thermodynamics] from [[Roger Ebert]]'s website.

[[Category:Cartoon physics|*]]

[[ja:マンガ物理学]]
[[zh:动画物理学]]

Physik in Animationsfilmen

2006-06-09T06:48:05Z

Simetrical: Style

'''Cartoon physics''' is a joking reference to the fact that [[animation]] allows regular [[law of physics|laws of physics]] to be ignored in [[humor|humorous]] ways. For example, when a cartoon character runs off a cliff, [[gravity]] has no effect until the character notices and mugs an appropriate reaction.<ref name="coyotusinterruptus">In a [[neologism]] contest held by ''[[New Scientist]]'', a winning entry coined the term "coyotus interruptus" for this phenomenon—a pun on [[coitus interruptus]] and [[Wile E. Coyote]], who fell to his doom this way particularly often.</ref>

The phrase also reflects the fact that many of the most famous [[United States|American]] [[animated cartoon]]s, particularly those from [[Warner Brothers]] and [[MGM]] studios, unconsciously developed a relatively consistent set of such "laws" that have become regularly applied in comic animation.

The idea that cartoons behave differently, but not randomly, than the real world is virtually as old as animation. [[Walt Disney]], for example, spoke of the ''plausible impossible'' (see [[The Plausible Impossible]], 1956), deliberately mispronouncing the second word so it rhymed with the first.

Specific reference to cartoon physics extends back at least to June of [[1980]], when an article "O'Donnell's Laws of Cartoon Motion"<ref>O'Donnell's Laws of Cartoon Motion", ''Esquire'', 6/80, reprinted in ''IEEE Institute'', 10/94; V.18 #7 p.12. [http://remarque.org/~doug/cartoon-physics.html Copy on Web]</ref> appeared in ''[[Esquire magazine]]''. A version printed in [[1994]] by the [[IEEE]] in a journal for [[engineering|engineers]] helped spread the word among the technical crowd, which has expanded and refined the idea. Dozens of websites exist outlining these laws.

The situation is so well-understood that it has been used as the topic of jokes for decades, as in the 1949 [[Looney Tunes]] short ''[[High Diving Hare]]'', in which [[Bugs Bunny]] explains, "I know this defies the law of gravity; but you see, I haven't studied law!"

More recently, the cartoon characters [[Roger Rabbit]] and [[Bonkers (TV series)|Bonkers D. Bobcat]] have their own variations on the theme, explaining that [[toon]]s are allowed to bend or break natural laws for the purposes of comedy. Doing this is extremely tricky, so [[toon]]s have a natural sense of comedic timing, giving them inherently funny properties. Bonkers also warns that the loss of this sense can lead to unfunny and even dangerous situations, perhaps explaining why cartoon violence, but not the real variety, is always funny.

In 1993, [[Stephen J. Gould]] writing in ''[[New Scientist]]'' noted that "... new, looney toon analysis reveals that these, seemingly nonsensical, phenomena can be described by logical laws similar to those in our world. Nonsensical events are by no means limited to the Looniverse. Laws that govern our own Universe often seem contrary to common sense."<ref>Stephen J. Gould, [http://www.newscientist.com/article/mg14019055.200.html Looney Tuniverse: There is a crazy kind of physics at work in the world of cartoons] (1993) ''New Scientist''</ref>. This theme is further described by Dr. Alan Cholodenko in his article, "The Nutty Universe of Animation" <ref>Dr. Alan Cholodenko, "[http://www.ubishops.ca/baudrillardstudies/vol3_1/cholodenkopf.htm The Nutty Universe of Animation, The “Discipline” of All “Disciplines”, And That’s Not All, Folks!]" ''International Journal of Baudrillard Studies'' Volume 3, Number 1 (January 2006)</ref>

== Why is it funny? ==

Adherents of [[evolutionary psychology]] have suggested that the humorous effect of cartoon physics is due to the interplay of intuitions between [[physics]] (objective) and [[psychology]] (self-perception). The physics module predicts that the cartoon character will fall over the cliff immediately, while the psychology module anthropomorphizes the force of gravity and thus see it as vulnerable to deception, as long as the actor is self-deceived {{cite needed}}.

In short, it can lead to the humorous situation where a cartoon's logic is governed by what "makes sense" (is consistent) rather than what "is" (natural law).

== Examples ==
Commonly cited cartoon physics "laws" include:

* No matter what happens to [[cat]]s, they always return to their default shapes.
* Any body passing through solid matter will leave a dent or cutout conforming to its perimeter.
* [[Explosive material|Explosives]], even if detonated close to a character's face, will cause only scorching of the skin. (Prior to the efforts of the [[American Civil Rights Movement]], characters would often take on the appearance of [[blackface]].) Similarly, a gun discharged directly into the face will not fire an actual bullet.
* If a character walks off a cliff, they will not fall, and continue to walk on thin air, until they notice they have walked off the cliff. In some cases a character can avoid falling, even if they are aware there is no ground below them.
* Alternatively, when a character runs off a cliff, notices the situation, and begins falling, at first only the body below the neck falls, during which the neck is stretched for a few seconds before the head follows.
* If a character falls from a tall building, another character from the same floor will be able to run all the way down to ground level in order to catch the falling character before he/she hits the ground.
* Characters are allowed to "swim" or blow themselves upwards a short distance in the air before falling normally to gravity.
* When a character chops the only thing holding another character from falling (such as a tree branch) the chopper will fall, together with whatever he/she was standing on (such as the tree or the ground) and the other character will remain floating in the air (branch included).
* An explosive device taken by one character will not explode until it is given back to the original character who triggered the device. Also applies to [[booby traps]].
* A [[boomerang]], when thrown, will not only change direction, but will actively hunt out its thrower so that the thrower may catch it (or be hit by it), regardless of his or her relation to the initial point of the throw.
* Motion reference frames are arbitrary. For instance, an outboard motor in a pan of water on wheels causes the motor and pan to move together. Likewise, a fan and a sail attached to a wheeled platform will cause the platform to move.
* A gun may be fired any number of times without being reloaded.
* Any fall is survivable.
* [[Cartoon hole|Holes]] can be physically picked up and moved. This also applies to mouths.

== Anvilology ==
'''Anvilology'''{{fact}} is the study of (cartoon) physical principles of [[anvil]]s, as studied at "Acme Looniversity" in the animated series, ''[[Tiny Toons]]''.
* Everything falls faster than an anvil (so that the evil character can hit the ground first and then be crushed, but not killed, by the anvil).
* Anvils are readily available.
* Anvils have [[mass]] but not much [[weight]], so that they are very hard to push around, but it is possible to jump out of a plane with an anvil instead of a parachute and not notice until the parachute is opened while airborne.
* Anvils can stay in the air until noticed by a character, at which point they fall on the character.
* If a character moves out of the way of a falling anvil, the anvil will shift its position over the character before falling, so that it crushes (but does not kill) the character.

== Cartoon collision physics ==

'''Cartoon collision physics''' are a subset of cartoon physics regarding the laws of collisions. Note that these laws deliberately refer to male subjects; bad things do not generally happen to women.

For a given cartoon character C:
* 1. If C runs into a wall,
:a: If the wall is too thick, C will strike it and flatten out like [[dough]], often regardless of clothing.
:b: If the wall is thin enough, he will leave a hole in the wall in the shape of his body.
* 2. If C runs into something made of metal, he will dent it in the shape of his body.
* 3. If C runs off a cliff, the [[impact crater]] he leaves will conform with Rule 1b.
* 4. If C has a fragile body,
:a: Running into any wall will cause him to be squashed into a [[musical instrument]] (usually an [[accordion]]), or
:b: Any collision or fall will fracture him into a [[zillion]] pieces.
* 5. If C runs into a wall which has been painted to look like part of the landscape or a tunnel:
:a: If the "camera" angle blends the painting with the actual landscape, he will enter the landscape or tunnel as though it were real.
:b: If he was the one who painted the wall, he will just run into the wall — see Rule 1.
:c: If the "camera" views the painting at an angle such that it is, without doubt, a painting on a wall, he will just run into the wall — see Rule 1.
:d: Trains or large trucks are often known to drive out of walls painted in this way, usually just after the painter has slammed into the wall and is feeling sheepish for having fallen for their own ruse. However, if the view of the oncoming vehicle is blocked, then the vehicle will apparently stop.

== Laws of Cartoon Thermodynamics ==

The Laws of Cartoon Thermodynamics are physical laws in the [[Animation|cartoon]] universe identified by [[Trevor Paquette]] and Lt. [[Justin D. Baldwin]] and popularized by film critic [[Roger Ebert]]. They overlap greatly with the older concept of "laws of [[cartoon physics]]".

*Any body suspended in space will remain in space until made aware of its situation (plus an interval for live falling bodies to express an appropriate emotion).
*Any body in motion will tend to remain in motion until solid matter intervenes suddenly.
*Any body passing through solid matter will leave a perforation conforming to its perimeter.
*The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken.
*All principles of gravity are negated by fear.
*As speed increases, objects can be in several places at once.
*Certain bodies can pass through solid walls painted to resemble tunnel entrances; others cannot.
*Any violent rearrangement of feline matter is impermanent.
*Everything falls faster than an anvil.
*Guns, no matter how powerful, or no matter where aimed, will do nothing more than char flesh, blow away feathers, or rearrange beaks. In certain ocasions, they leave a perfectly circular hole that goes completely through the body of the character being shot, but this does not affect his/her health in any way.
*Any given amount of explosives will propel a body miles away, but still in one piece, charred and extremely peeved.
* Arms holding large falling weights are infinitely elastic, but will eventually drag the holder along.

== Anime physics ==

[[Anime]] physics can be considered a subset of cartoon physics - a set of rules used in cartoons to twist or ignore the laws of physics for humorous or dramatic effect. These are commonly seen in anime but not so common in cartoons. Normally, these are referenced from popular series in the past.
Note that many of these laws only apply to [[shounen]] series.

Examples include:

*Dramatic moments tend to distort time, either by slowing it down (usually long enough to call out the name of an attacker or the name of the "special move" used in the attack, or for bystanders to comment on the situation), or by looping three times.
**Similarly, transformations (especially those animated with [[stock footage]]) also seem to stop time until completed, allowing them to be used to counter attacks, or not allowing the person to be attacked while performing them.

*An angry or embarrassed girl will be able to hit any male (usually one who is romantically involved with her) hard enough to knock him into [[low Earth orbit]] and the male will usually survive.

*Attacks strong enough to shred entire planets will not destroy anyone's pants (but will usually destroy all other clothing). Conversely, certain explosions can destroy a female character's clothing without significantly harming her body—in some cases, without her initially noticing this.

*Any fire-based attack on a character will not completely burn his/her clothes but will leave black stains instead.

== Notes ==
<references />

== External links ==
*[http://funnies.paco.to/cartoon.html Cartoon Laws of Physics]
*[http://www.cs.utah.edu/~duongsaa/more_htm/jk_100animeRules.htm 100 Laws of Anime Physics]
*[http://www.animeinfo.org/animeu/phys101.html Animeinfo.org: Anime Physics]
*[http://www.abcb.com/laws The Laws of Anime]
*[http://rogerebert.suntimes.com/apps/pbcs.dll/article?AID=/20050210/GLOSSARY/50213001/1005 Laws of Cartoon Thermodynamics] from [[Roger Ebert]]'s website.

[[Category:Cartoon physics|*]]

[[ja:マンガ物理学]]
[[zh:动画物理学]]

Berry-Paradoxon

2006-04-23T03:55:03Z

Simetrical: /* Resolution of the paradox */ I don't think "twenty-one" is two words, at least not in common usage.

The '''Berry paradox''' is the apparent contradiction that arises from expressions such as the following:

:''The smallest positive [[integer]] not nameable in under eleven words.''

We can argue that this phrase specifies a unique integer as follows: there are [[Finite set|finitely]] many phrases of fewer than eleven words. Some of these phrases denote a unique integer: For example, "one hundred thirty six", "the smallest prime number greater than five hundred million" or "ninety raised to the [[centillion]]th power". On the other hand, some of these phrases denote things which are not integers—for example, "[[Tony Blair]]" or "[[M1 Abrams|M1A2 Abrams Main Battle Tank]]". In any case, the set '''A''' of integers that can be uniquely specified in under eleven words is finite. Since '''A''' is finite, not every positive integer can be in '''A'''. Thus by [[well-ordering]] of the integers, there is a smallest positive integer that is not in '''A'''.

But the Berry expression itself is a specification for that number in only ten words!

This is clearly [[paradox]]ical, and would seem to suggest that "nameable in under eleven words" may not be well-defined. However, using programs or proofs of bounded lengths, it is possible to construct an analogue of the Berry expression in a formal mathematical language, as has been done by [[Gregory Chaitin]]. Though the formal analogue does not lead to a logical contradiction, it does prove certain impossibility results, including an incompleteness theorem similar in spirit to [[Gödel's incompleteness theorem]]; see [[Kolmogorov complexity]] for details.

The Berry paradox was proposed by [[Bertrand Russell]] (Russell, 1906). He attributed it to [[G. G. Berry]] of the [[Bodleian library]] (c.f. Russell and Whitehead 1910), who had suggested the idea of considering the paradox associated to the expression "the first undefinable [[ordinal number|ordinal]]".

== Resolution of the paradox ==
It is generally accepted that the Berry paradox and other similar paradoxes (such as the [[Richard's paradox]]) result from interpreting sets of possibly self-referential expressions. According to (Russell and Whitehead, 1910) these paradoxes "embody vicious circle fallacies". To resolve one of these paradoxes means to pinpoint exactly where our use of language went wrong and to provide restrictions on the use of language which may avoid them.

Note that some Berry type expressions present only minor problems of interpretation:

: ''The smallest positive integer not nameable in under two words.''

denotes 101 (or arguably 21), since "hundred one" is two [[Word (linguistics)|word]]s (as "twenty-one" may be by linguistic standards, if not the common standards of English speakers) and any indirect definition of the number (such as "the number of dots on a six-sided die", or indeed "the smallest positive integer not nameable in under two words") is necessarily two or more words long.

However, Berry's paradox ''can'' be forced into a formal system. Boolos used a specific formalization to provide an alternate proof of [[Godel's Incompleteness Theorem]]. The basic idea of the proof is that a [[proposition]] that holds of ''x'' if ''x'' = ''n'' for some natural number ''n'' can be called a "name" for ''n'', and that the set {(''n'', ''k''): the natural number ''n'' has a name that is ''k'' symbols long} can be shown to be representable (using Gödel numbers). Then the proposition "''m'' is the first number not nameable in under ''k'' symbols" can be formalized and shown to be a name.

==References==
* Charles H. Bennett, ''On Random and Hard-to-Describe Numbers'', IBM Report RC7483 (1979) http://www.research.ibm.com/people/b/bennetc/Onrandom.pdf
* George Boolos, ''A new proof of the Gödel Incompleteness Theorem.'' ''Notices of the American Mathematical Society'', 36(4), pp. 388-390.
* Bertrand Russell, ''Les paradoxes de la logique'', Revue de métaphysique et de morale, vol 14, pp 627-650
* Bertrand Russell and Alfred N. Whitehead, ''Principia Mathematica'', Cambridge University Press/ A paperback reissue up to *56 was published in 1962.

== See also ==
* [[Definable number]]
* [[Busy beaver]]

==External links==
* http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unm2.html A discussion by [[Gregory Chaitin]]
* http://www.cs.yorku.ca/~peter/Berry.html
* http://mathworld.wolfram.com/BerryParadox.html The entry for the Berry paradox at [[Wolfram Research|Wolfram Research's]] [[MathWorld]]
* http://www.hgsc.bcm.tmc.edu/~kdurbin/texts/alg.info.chiatin.html

[[Category:Paradoxes]]

[[fr:Paradoxe de Berry]]
[[he:הפרדוקס של ברי]]
[[ja:ベリーのパラドックス]]
[[pl:Paradoks nieciekawej liczby]]
[[it:Paradosso di Berry]]

Berry-Paradoxon

2006-04-23T03:50:49Z

Simetrical: We can be more creative than to name two people

The '''Berry paradox''' is the apparent contradiction that arises from expressions such as the following:

:''The smallest positive [[integer]] not nameable in under eleven words.''

We can argue that this phrase specifies a unique integer as follows: there are [[Finite set|finitely]] many phrases of fewer than eleven words. Some of these phrases denote a unique integer: For example, "one hundred thirty six", "the smallest prime number greater than five hundred million" or "ninety raised to the [[centillion]]th power". On the other hand, some of these phrases denote things which are not integers—for example, "[[Tony Blair]]" or "[[M1 Abrams|M1A2 Abrams Main Battle Tank]]". In any case, the set '''A''' of integers that can be uniquely specified in under eleven words is finite. Since '''A''' is finite, not every positive integer can be in '''A'''. Thus by [[well-ordering]] of the integers, there is a smallest positive integer that is not in '''A'''.

But the Berry expression itself is a specification for that number in only ten words!

This is clearly [[paradox]]ical, and would seem to suggest that "nameable in under eleven words" may not be well-defined. However, using programs or proofs of bounded lengths, it is possible to construct an analogue of the Berry expression in a formal mathematical language, as has been done by [[Gregory Chaitin]]. Though the formal analogue does not lead to a logical contradiction, it does prove certain impossibility results, including an incompleteness theorem similar in spirit to [[Gödel's incompleteness theorem]]; see [[Kolmogorov complexity]] for details.

The Berry paradox was proposed by [[Bertrand Russell]] (Russell, 1906). He attributed it to [[G. G. Berry]] of the [[Bodleian library]] (c.f. Russell and Whitehead 1910), who had suggested the idea of considering the paradox associated to the expression "the first undefinable [[ordinal number|ordinal]]".

== Resolution of the paradox ==
It is generally accepted that the Berry paradox and other similar paradoxes (such as the [[Richard's paradox]]) result from interpreting sets of possibly self-referential expressions. According to (Russell and Whitehead, 1910) these paradoxes "embody vicious circle fallacies". To resolve one of these paradoxes means to pinpoint exactly where our use of language went wrong and to provide restrictions on the use of language which may avoid them.

Note that some Berry type expressions present only minor problems of interpretation:

: ''The smallest positive integer not nameable in under two words.''

under reasonable definitions of English denotes 21, since "twenty one" is two words and any indirect definition of the number (such as "the number of dots on a six-sided die", or indeed "the smallest positive integer not nameable in under two words") is necessarily two or more words long.

However, Berry's paradox ''can'' be forced into a formal system. Boolos used a specific formalization to provide an alternate proof of [[Godel's Incompleteness Theorem]]. The basic idea of the proof is that a [[proposition]] that holds of ''x'' if ''x'' = ''n'' for some natural number ''n'' can be called a "name" for ''n'', and that the set {(''n'', ''k''): the natural number ''n'' has a name that is ''k'' symbols long} can be shown to be representable (using Gödel numbers). Then the proposition "''m'' is the first number not nameable in under ''k'' symbols" can be formalized and shown to be a name.

==References==
* Charles H. Bennett, ''On Random and Hard-to-Describe Numbers'', IBM Report RC7483 (1979) http://www.research.ibm.com/people/b/bennetc/Onrandom.pdf
* George Boolos, ''A new proof of the Gödel Incompleteness Theorem.'' ''Notices of the American Mathematical Society'', 36(4), pp. 388-390.
* Bertrand Russell, ''Les paradoxes de la logique'', Revue de métaphysique et de morale, vol 14, pp 627-650
* Bertrand Russell and Alfred N. Whitehead, ''Principia Mathematica'', Cambridge University Press/ A paperback reissue up to *56 was published in 1962.

== See also ==
* [[Definable number]]
* [[Busy beaver]]

==External links==
* http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unm2.html A discussion by [[Gregory Chaitin]]
* http://www.cs.yorku.ca/~peter/Berry.html
* http://mathworld.wolfram.com/BerryParadox.html The entry for the Berry paradox at [[Wolfram Research|Wolfram Research's]] [[MathWorld]]
* http://www.hgsc.bcm.tmc.edu/~kdurbin/texts/alg.info.chiatin.html

[[Category:Paradoxes]]

[[fr:Paradoxe de Berry]]
[[he:הפרדוקס של ברי]]
[[ja:ベリーのパラドックス]]
[[pl:Paradoks nieciekawej liczby]]
[[it:Paradosso di Berry]]

Emilia Lanier

2005-12-14T04:53:15Z

Simetrical: Revert unsourced anon edit

'''Aemilia Lanyer''', or '''Emilia Lanier''' ([[1569]]-[[1645]]) was the first Englishwoman to assert herself as a professional poet through her single volume of poems, ''Salve Deus Rex Judaeorum'' ([[1611]]). The volume is prefaced by eleven dedicatory works all to women, centered by a title poem on Christ's passion narrated entirely from the point of view of women, and concludes with "A Description of Cookham," dedicated to Margaret, Countess of Cumberland and her daughter Lady Anne Clifford. This last is the first published country house poem in English (Ben Jonson's more famous "To Penshurst" may have been written earlier but was first published in 1616).

Born '''Aemilia Bassano''', Lanyer was a member of the minor gentry through her father's appointment as a royal musician, and was apparently educated in the household of the dowager Countess of Kent. She was for several years the mistress of Queen Elizabeth's cousin, Henry Cary, Lord Hunsdon, and was married to court musician Alfonso Lanyer in 1592 when she became pregnant.

After Aemilia was no longer at court, Lord Hunsdon became the patron of [[William Shakespeare]]'s theatre company and some have speculated that Lanyer, an apparently striking woman who had Bassano cousins described as having dark hair, was Shakespeare's "[[Dark Lady]]". The scholarly consensus is that this is unlikely, and more recently attenion has focused on her poetry. "A Description of Cookham," for example, is the first published country house poem in English, and is often compared with Ben Jonson's "To Penshurst."

[[Category:1569 births|Lanier, Emilia]]
[[Category:1645 deaths|Lanier, Emilia]]
[[Category:William Shakespeare|Lanier, Emilia]]
[[Category:English poets|Lanier, Emilia]]
[[Category:Women poets|Lanier, Emilia]]

Novantae

2005-12-14T04:40:04Z

Simetrical: Popups-assisted disambiguation from Roman to ancient Rome

The Novantae were a [[Celtic]] tribe located in [[Galloway]] in modern [[Scotland]]. To be more precise, their base was around the [[Rhins of Galloway]], a southern peninsula jutting into the [[Irish Sea]]. The tribe was known to the [[ancient Rome|Romans]] as a trading partner. Little more is known about the tribe, which was a farming, herding and trading society, as opposed to the stereotypical warring clans of [[Caledonia]].

See also [[List_of_Celtic_tribes]].

Sources: http://www.undiscoveredscotland.co.uk/whithorn/whithorn/index.html
http://www.unrv.com/forum/index.php?act=ST&f=4&t=88&

Kyōiku-Kanji

2005-12-14T03:17:13Z

Simetrical: Revert

{{Japanese writing}}

'''''Kyōiku kanji''''' (教育漢字, lit. "education kanji"), also known as '''''Gakunenbetsu kanji haitōhyō''''' (学年別漢字配当表, lit. "list of kanji by school year") is a list of 1,006 [[kanji]] and associated readings developed and maintained by the [[Japan]]ese Ministry of Education that prescribes which kanji, and which readings of kanji, Japanese schoolchildren should learn for each year of elementary school. Although the list is designed for Japanese children, it can also be used as a sequence of learning characters by non-native speakers in order to limit the kanji to the most commonly used.

==Versions of kyōiku list==
*[[1946]] created with 881 characters
*[[1977]] expanded to 996 characters
*[[1982]] expanded to 1,006 characters by adding ten Roman (that is, Arabic) numerals

(In some contexts, the term ''gakushū kanji'' "study characters" is used to refer to the list of 1,006 and the term ''kyōiku kanji'' reserved for the list of 996 without the roman numerals.)

==The list by grade==

===First grade (80 kanji)===
*[[wiktionary:一|一]] one ''ichi''
*[[wiktionary:二|二]] two ''ni''
*[[wiktionary:三|三]] three ''san''
*[[wiktionary:四|四]] four ''shi'' or ''yon''
*[[wiktionary:五|五]] five ''go''
*[[wiktionary:六|六]] six ''roku''
*[[wiktionary:七|七]] seven ''shichi'' or ''nana''
*[[wiktionary:八|八]] eight ''hachi''
*[[wiktionary:九|九]] nine ''kū'' or ''kyū''
*[[wiktionary:十|十]] ten ''jū''
*[[wiktionary:百|百]] hundred ''hyaku''
*[[wiktionary:千|千]] thousand ''sen''
*[[wiktionary:上|上]] up ''ue''
*[[wiktionary:下|下]] below ''shita''
*[[wiktionary:左|左]] left ''hidari''
*[[wiktionary:右|右]] right ''migi''
*[[wiktionary:中|中]] middle or inside ''naka''
*[[wiktionary:大|大]] large ''dai'' or ''ō-kii''
*[[wiktionary:小|小]] small ''shō'' or ''chii-sai''
*[[wiktionary:月|月]] month; moon ''gatsu'' or ''tsuki
*[[wiktionary:日|日]] day ''hi'' or ''nichi''
*[[wiktionary:年|年]] year ''nen'' or ''toshi''
*[[wiktionary:早|早]] early ''sō'' or ''haya-i''
*[[wiktionary:木|木]] tree ''moku'' or ''ki''
*[[wiktionary:林|林]] woods ''rin'' or ''hayashi''
*[[wiktionary:山|山]] mountain ''san'' or ''yama''
*[[wiktionary:川|川]] river ''sen'' or ''kawa''
*[[wiktionary:土|土]] soil ''do'' or ''tsuchi''
*[[wiktionary:空|空]] sky ''kū'' or ''sora''
*[[wiktionary:田|田]] rice paddy ''den'' or ''ta''
*[[wiktionary:天|天]] heaven ''ten'' or ''ama''
*[[wiktionary:生|生]] life ''sei'' or ''i-kiru''
*[[wiktionary:花|花]] flower ''ka'' or ''hana''
*[[wiktionary:草|草]] grass ''sō'' or ''kusa''
*[[wiktionary:虫|虫]] insect ''chū'' or ''mushi''
*[[wiktionary:犬|犬]] dog ''ken'' or ''inu''
*[[wiktionary:人|人]] person ''jin'' or ''nin'' or ''hito''
*[[wiktionary:名|名]] name ''na'' or ''mei'' or ''myo''
*[[wiktionary:女|女]] female ''nyo'' or ''onna''
*[[wiktionary:男|男]] male ''dan'' or ''otoko''
*[[wiktionary:子|子]] child ''ko''
*[[wiktionary:目|目]] eye ''moku'' or ''me''
*[[wiktionary:耳|耳]] ear ''ji'' or ''mimi''
*[[wiktionary:口|口]] mouth ''kō'' or ''kuchi''
*[[wiktionary:手|手]] hand ''shu'' or ''te''
*[[wiktionary:足|足]] foot or leg ''soku'' or ''ashi''
*[[wiktionary:見|見]] see ''ken'' or ''mi-ru''
*[[wiktionary:音|音]] sound ''on'' or ''ne'' or ''oto''
*[[wiktionary:力|力]] power ''riki'' or ''ryoku'' or ''chikara''
*[[wiktionary:気|気]] spirit''ki''
*[[wiktionary:円|円]] yen or circle ''en''
*[[wiktionary:入|入]] enter ''nyū'' or ''hai-ru'' or ''i-ru''
*[[wiktionary:出|出]] exit ''shutsu'' or ''de-ru''
*[[wiktionary:立|立]] stand up ''ritsu'' or ''ta-tsu''
*[[wiktionary:休|休]] rest ''kyū'' or ''yasu-mu''
*[[wiktionary:先|先]] previous ''sen'' or ''saki''
*[[wiktionary:夕|夕]] evening ''yū''
*[[wiktionary:本|本]] book ''hon'' or ''moto''
*[[wiktionary:文|文]] writing ''fumi'' or ''bun'' or ''mo''
*[[wiktionary:字|字]] character ''ji''
*[[wiktionary:学|学]] study ''gaku'' or ''mana-bu''
*[[wiktionary:学|学]][[wiktionary:校|校]] school ''gakkō''
*[[wiktionary:村|村]] village ''son'' or ''mura''
*[[wiktionary:町|町]] town ''chō'' or ''machi''
*[[wiktionary:森|森]] forest ''shin'' or ''mori''
*[[wiktionary:正|正]] correct ''sei'' or ''tada-shii''
*[[wiktionary:水|水]] water ''sui'' or ''mizu''
*[[wiktionary:火|火]] fire ''ka'' or ''hi''
*[[wiktionary:玉|玉]] ball ''gyoku'' or ''tama''
*[[wiktionary:王|王]] king ''ō''
*[[wiktionary:石|石]] stone ''seki'' or ''ishi''
*[[wiktionary:竹|竹]] bamboo ''chiku'' or ''take''
*[[wiktionary:糸|糸]] thread ''shi'' or ''ito''
*[[wiktionary:貝|貝]] shellfish ''kai''
*[[wiktionary:車|車]] car ''sha'' or ''kuruma''
*[[wiktionary:金|金]] gold ''kin'' or ''kane''
*[[wiktionary:雨|雨]] rain ''u'' or ''ame''
*[[wiktionary:赤|赤]] red ''seki'' or ''aka''
*[[wiktionary:青|青]] blue ''sei'' or ''ao''
*[[wiktionary:白|白]] white ''haku'' or ''shiro''

===Second grade (160 kanji)===
*[[wiktionary:数|数]] number ''sū'' or ''kazu''
*[[wiktionary:多|多]] many or much ''ta'' or ''oo-i''
*[[wiktionary:少|少]] a few or a little ''shō'' or ''suku-nai'' or ''suko-shi''
*[[wiktionary:万|万]] ten thousand ''man''
*[[wiktionary:半|半]] half ''han'' or ''naka-ba''
*[[wiktionary:形|形]] shape ''kei'' or ''katachi''
*[[wiktionary:太|太]] fat ''ta'' or ''futo-i''
*[[wiktionary:細|細]] thin ''sai'' or ''hoso-i''
*[[wiktionary:広|広]] wide ''kō'' or ''hiro-i''
*[[wiktionary:長|長]] long ''chō'' or ''naga-i''
*[[wiktionary:点|点]] point ''ten''
*[[wiktionary:丸|丸]] circle ''gan'' or ''maru''
*[[wiktionary:交|交]] cross ''kō'' or ''maji''
*[[wiktionary:光|光]] light ''kō'' or ''hikari''
*[[wiktionary:角|角]] angle or corner ''kaku'' or ''kado'' or ''tsuno''
*[[wiktionary:計|計]] measure ''kei'' or ''haka-ru''
*[[wiktionary:直|直]] straight or correct ''choku'' or ''nao-su''
*[[wiktionary:線|線]] line ''sen''
*[[wiktionary:矢|矢]] arrow ''ya''
*[[wiktionary:弱|弱]] weak ''jaku'' or ''yowa-i''
*[[wiktionary:強|強]] strong ''kyō'' or ''tsuyo-i''
*[[wiktionary:高|高]] tall or high ''kō'' or ''taka-i''
*[[wiktionary:同|同]] same ''dō'' or ''ona-ji''
*[[wiktionary:親|親]] parent ''shin'' or ''oya''
*[[wiktionary:母|母]] mother ''haha'' or ''kaa'' (as in ''お母さん'' ''okaasan'')
*[[wiktionary:父|父]] father ''chichi'' or ''tou'' (as in ''お父さん'' ''otousan'')
*[[wiktionary:姉|姉]] older sister ''shi'' or ''ane''
*[[wiktionary:兄|兄]] older brother ''kei'' or ''ani''
*[[wiktionary:弟|弟]] younger brother ''tei'' or ''otouto''
*[[wiktionary:妹|妹]] younger sister ''mai'' or ''imōto''
*[[wiktionary:自|自]] oneself ''ji''
*[[wiktionary:友|友]] friend ''yū'' or ''tomo''
*[[wiktionary:体|体]] body ''tai'' or ''karada''
*[[wiktionary:毛|毛]] hair ''mō'' or ''ke''
*[[wiktionary:頭|頭]] head ''tō'' or ''atama''
*[[wiktionary:顔|顔]] face ''gan'' or ''kao''
*[[wiktionary:首|首]] neck ''shu'' or ''kubi''
*[[wiktionary:心|心]] heart ''shin'' or ''kokoro''
*[[wiktionary:時|時]] time ''ji'' or ''toki''
*[[wiktionary:曜|曜]] weekday ''yō''
*[[wiktionary:朝|朝]] morning ''chō'' or ''asa''
*[[wiktionary:昼|昼]] daytime ''chū'' or ''hiru''
*[[wiktionary:夜|夜]] night ''ya'' or ''yoru''
*[[wiktionary:分|分]] minute; understand ''fun'' or ''wa'' (as in ''分かる wakaru'', to understand)
*[[wiktionary:週|週]] week　''shū''
*[[wiktionary:春|春]] spring ''shun'' or ''haru''
*[[wiktionary:夏|夏]] summer ''ka'' or ''natsu''
*[[wiktionary:秋|秋]] autumn ''shū'' or ''aki''
*[[wiktionary:冬|冬]] winter ''tō'' or ''fuyu''
*[[wiktionary:今|今]] now ''kon'' or ''ima''
*[[wiktionary:新|新]] new ''shin'' or ''atara-shii''
*[[wiktionary:古|古]] old ''ko'' or ''furu-i''
*[[wiktionary:間|間]] interval ''kan'' or ''ma'' or ''aida''
*[[wiktionary:方|方]] direction ''hō'' or ''kata''
*[[wiktionary:北|北]] north ''hoku'' or ''kita''
*[[wiktionary:南|南]] south ''nan'' or ''minami''
*[[wiktionary:東|東]] east ''tō'' or ''higashi'' or ''azuma''
*[[wiktionary:西|西]] west ''sei'' or ''sai'' or ''nishi''
*[[wiktionary:遠|遠]] far　''en'' or ''tō-i''
*[[wiktionary:近|近]] near ''kin'' or ''chika-i''
*[[wiktionary:前|前]] in front ''zen'' or ''mae''
*[[wiktionary:後|後]] behind ''go'' or ''ushi-ro''
*[[wiktionary:内|内]] inside ''nai'' or ''uchi''
*[[wiktionary:外|外]] outside ''gai'' or ''soto''
*[[wiktionary:場|場]] place ''jō'' or ''ba''
*[[wiktionary:地|地]] ground ''chi''
*[[wiktionary:国|国]] country ''koku'' or ''kuni''
*[[wiktionary:園|園]] garden ''en'' or ''sono''
*[[wiktionary:谷|谷]] valley ''koku'' or ''tani''
*[[wiktionary:野|野]] field ''ya'' or ''no''
*[[wiktionary:原|原]] field ''gen'' or ''hara''
*[[wiktionary:里|里]] village ''ri'' or ''sato''
*[[wiktionary:市|市]] city ''shi'' or ''ichi''
*[[wiktionary:京|京]] capital ''kyō''
*[[wiktionary:風|風]] wind ''fū'' or ''kaze''
*[[wiktionary:雪|雪]] snow ''setsu'' or ''yuki''
*[[wiktionary:雲|雲]] cloud ''un'' or ''kumo''
*[[wiktionary:池|池]] pond ''chi'' or ''ike''
*[[wiktionary:海|海]] sea ''kai'' or ''umi''
*[[wiktionary:岩|岩]] rock ''gan'' or ''iwa''
*[[wiktionary:星|星]] star ''sei'' or ''hoshi''
*[[wiktionary:室|室]] room ''shitsu'' or ''muro''
*[[wiktionary:戸|戸]] door ''to'' or ''ko'' or ''be''
*[[wiktionary:家|家]] house ''ka'' or ''ke'' or ''ie''
*[[wiktionary:寺|寺]] Buddhist temple ''ji'' or ''tera''
*[[wiktionary:通|通]] pass through ''tsū'' or ''tō-ru''
*[[wiktionary:門|門]] gates ''mon'' or ''kado''
*[[wiktionary:道|道]] road ''dō'' or ''michi''
*[[wiktionary:話|話]] talk ''wa'' or ''hana-su''
*[[wiktionary:言|言]] say ''gen'' or ''i-u''
*[[wiktionary:答|答]] answer ''tō'' or ''kota-eru''
*[[wiktionary:声|声]] voice ''sei'' or ''koe''
*[[wiktionary:聞|聞]] hear ''chō'' or ''ki-ku''
*[[wiktionary:語|語]] language ''go''
*[[wiktionary:読|読]] read ''doku'' or ''yo-mu''
*[[wiktionary:書|書]] write ''sho'' or ''ka-ku''
*[[wiktionary:記|記]] write down ''ki''
*[[wiktionary:紙|紙]] paper　''shi'' or ''kami''
*[[wiktionary:画|画]] picture ''ga''
*[[wiktionary:絵|絵]] picture ''kai'' or ''e''
*[[wiktionary:図|図]] drawing ''zu'' or ''haka-ru''
*[[wiktionary:工|工]] craft ''kō''
*[[wiktionary:教|教]] teach ''kyō'' or ''oshi-eru''
*[[wiktionary:晴|晴]] fine ''sei'' or ''hare''
*[[wiktionary:思|思]] think ''shi'' or ''omo-u''
*[[wiktionary:考|考]] think about ''kō'' or ''kanga-eru''
*[[wiktionary:知|知]] know ''chi'' or ''shi-ru''
*[[wiktionary:才|才]] ability or years old ''sai''
*[[wiktionary:理|理]] reason ''ri'' or ''kotowari''
*[[wiktionary:算|算]] calculate ''san''
*[[wiktionary:作|作]] make ''saku'' or ''tsuku-ru''
*[[wiktionary:元|元]] origin ''gen'' or ''moto''
*[[wiktionary:食|食]] eat, meal ''shoku'' or ''tabe-ru''
*[[wiktionary:肉|肉]] meat ''niku''
*[[wiktionary:馬|馬]] horse ''ba'' or ''uma''
*[[wiktionary:牛|牛]] cow ''gyū'' or ''ushi''
*[[wiktionary:魚|魚]] fish ''gyō'' or ''sakana''
*[[wiktionary:鳥|鳥]] bird ''chō'' or ''tori''
*[[wiktionary:羽|羽]] feather ''ha'' or ''wa'' or ''hane''
*[[wiktionary:鳴|鳴]] chirp ''mei'' or ''na-ku''
*[[wiktionary:麦|麦]] wheat ''baku'' or ''mugi''
*[[wiktionary:米|米]] rice ''bei'' or ''kome''
*[[wiktionary:茶|茶]] tea ''cha''
*[[wiktionary:色|色]] colour ''shoku'' or ''iro''
*[[wiktionary:黄|黄]] yellow ''ō'' or ''kiiro''
*[[wiktionary:黒|黒]] black ''koku'' or ''kuro''
*[[wiktionary:来|来]] come ''rai'' or ''ku-ru''
*[[wiktionary:行|行]] go ''gyō'' or ''kō'' or ''ik-u''
*[[wiktionary:帰|帰]] return home ''ki'' or ''kae-ru''
*[[wiktionary:歩|歩]] walk ''ho'' or ''aru-ku''
*[[wiktionary:走|走]] run ''sō'' or ''hashi-ru''
*[[wiktionary:止|止]] stop ''shi'' or ''to-maru''
*[[wiktionary:活|活]] active ''katsu'' or ''i-kiru''
*[[wiktionary:店|店]] store ''ten'' or ''mise''
*[[wiktionary:買|買]] buy ''bai'' or ''ka-u''
*[[wiktionary:売|売]] sell ''bai'' or ''ur-u''
*[[wiktionary:午|午]] noon, sign of the horse ([[Earthly Branches]]) ''go'' or ''uma''
*[[wiktionary:汽|汽]] steam ''ki''
*[[wiktionary:弓|弓]] bow (archery, violin) ''kyū'' or ''yumi''
*[[wiktionary:回|回]] -times, to revolve ''kai''
*[[wiktionary:会|会]] association ''kai'' or ''e''
*[[wiktionary:組|組]] association ''kumi''
*[[wiktionary:船|船]] ship ''sen'' or ''fune''
*[[wiktionary:明|明]] bright ''mei'' or ''aka-rui''
*[[wiktionary:社|社]] company ''sha'' or ''yashiro''
*[[wiktionary:切|切]] cut ''setsu'' or ''ki-ru''
*[[wiktionary:電|電]] electricity ''den''
*[[wiktionary:毎|毎]] every ''mai''
*[[wiktionary:合|合]] fit ''gō'' to ''a-u''
*[[wiktionary:当|当]] hit ''tō'' or ''a-taru''
*[[wiktionary:台|台]] base ''dai'' or ''tai''
*[[wiktionary:楽|楽]] pleasure ''raku'' or ''tano-shii''
*[[wiktionary:公|公]] public ''kou'' or ''ōyake''
*[[wiktionary:引|引]] pull ''in'' or ''hi-ku''
*[[wiktionary:科|科]] section ''ka''
*[[wiktionary:歌|歌]] song ''ka'' or ''uta''
*[[wiktionary:刀|刀]] katana ''tō'' or ''katana''
*[[wiktionary:番|番]] turn ''ban''
*[[wiktionary:用|用]] use ''yō'' or ''mochi-iru''
*[[wiktionary:何|何]] what ''nani''

===Third grade (200 kanji)===
*[[wiktionary:丁|丁]] pair ''chō''
*[[wiktionary:世|世]] world ''se'' or ''yo''
*[[wiktionary:両|両]] both ''ryō''
*[[wiktionary:主|主]] master ''shu'' or ''nushi''
*[[wiktionary:乗|乗]] ride ''jō'' or ''no-ru''
*[[wiktionary:予|予]] in advance ''yo'' or ''arakaji-me''
*[[wiktionary:事|事]] abstract thing ''ji'' or ''koto''
*[[wiktionary:仕|仕]] serve ''shi'' or ''tsuka-eru''
*[[wiktionary:他|他]] other ''ta'' or ''hoka''
*[[wiktionary:代|代]] substitute ''tai'' or ''kawa-ru''
*[[wiktionary:住|住]] dwell ''jū'' or ''su-mu''
*[[wiktionary:使|使]] use ''shi'' or ''tsuka-u''
*[[wiktionary:係|係]] person in charge ''kei'' or ''kakari''
*[[wiktionary:倍|倍]] double ''bai''
*[[wiktionary:全|全]] whole ''zen''
*[[wiktionary:具|具]] tool ''gu''
*[[wiktionary:写|写]] copy ''sha''
*[[wiktionary:列|列]] row ''retsu''
*[[wiktionary:助|助]] help ''jo'' or ''tasu-keru''
*[[wiktionary:勉|勉]] diligence ''ben''
*[[wiktionary:動|動]] move ''dou'' or ''ugo-ku''
*[[wiktionary:勝|勝]] win ''shō'' or ''kat-su''
*[[wiktionary:化|化]] disguise ''ka'' or ''ba-keru''
*[[wiktionary:区|区]] ward ''ku''
*[[wiktionary:医|医]] doctor ''i''
*[[wiktionary:去|去]] leave ''kyo'' or ''sa-ru''
*[[wiktionary:反|反]] anti- ''han'' or ''so-ru''
*[[wiktionary:取|取]] take ''shu''or ''to-ru''
*[[wiktionary:受|受]] receive ''ju'' or ''u-keru''
*[[wiktionary:号|号]] number ''gō''
*[[wiktionary:向|向]] face(v.) ''kō'' or ''mu-kau''
*[[wiktionary:君|君]] you ''kun'' or ''kimi''
*[[wiktionary:味|味]] flavor 'mi'' or ''aji''
*[[wiktionary:命|命]] life ''mei'' or ''inochi''
*[[wiktionary:和|和]] peace or sum ''wa'' or ''nago-mu''
*[[wiktionary:品|品]] article ''hin'' or ''shina''
*[[wiktionary:員|員]] member ''in''
*[[wiktionary:商|商]] commerce ''shō'' or ''akina-i''
*[[wiktionary:問|問]] question ''mon'' or ''toi'' or ''to-u''
*[[wiktionary:坂|坂]] slope ''han'' or ''saka''
*[[wiktionary:夫|夫]] husband ''hu'' or ''otto''
*[[wiktionary:始|始]] begin ''shi'' or ''haji-meru''
*[[wiktionary:委|委]] committee ''i''
*[[wiktionary:守|守]] protect ''shu'' or ''mamo-ru''
*[[wiktionary:安|安]] cheap ''an'' or ''yasu-i''
*[[wiktionary:定|定]] fix ''tei'' or ''sada-meru''
*[[wiktionary:実|実]] fruit or content ''jitsu'' or ''mi''
*[[wiktionary:客|客]] guest ''kaku'' or ''kyaku''
*[[wiktionary:宮|宮]] Shinto shrine or prince(princess) ''kyū'' or ''miya''
*[[wiktionary:宿|宿]] inn ''shuku'' or ''yado''
*[[wiktionary:寒|寒]]い cold ''kan'' or ''samu-i''
*[[wiktionary:対|対]] opposite ''tai'' or ''tsui''
*[[wiktionary:局|局]] office ''kyoku''
*[[wiktionary:屋|屋]] premise ''oku'' or ''ya''
*[[wiktionary:岸|岸]] shore ''gan'' or ''kishi''
*[[wiktionary:島|島]] island ''tō'' or ''shima''
*[[wiktionary:州|州]] state ''shū''
*[[wiktionary:帳|帳]] account book ''chō''
*[[wiktionary:平|平]] flat ''hei'' or ''tai-ra''
*[[wiktionary:幸|幸]] happiness ''kō'' or ''shiawa-se''
*[[wiktionary:度|度]] degrees ''do''
*[[wiktionary:庫|庫]] warehouse ''ko''
*[[wiktionary:庭|庭]] garden ''tei'' or ''niwa''
*[[wiktionary:式|式]] style ''shiki''
*[[wiktionary:役|役]] role ''eki'' or ''yaku''
*[[wiktionary:待|待]] wait ''tai'' or ''ma-tsu''
*[[wiktionary:急|急]] hurry ''kyū'' or ''iso-gu''
*[[wiktionary:息|息]] breath ''soku'' or ''iki''
*[[wiktionary:悪|悪]] bad ''aku'' or ''waru-i''
*[[wiktionary:悲|悲]] sad ''hi'' or ''kana-shii''
*[[wiktionary:想|想]] thought ''sō'' or ''omo-u''
*[[wiktionary:意|意]] idea ''i''
*[[wiktionary:感|感]] feel ''kan-jiru''
*[[wiktionary:所|所]] place ''sho'' or ''tokoro''
*[[wiktionary:打|打]] hit ''da'' or ''u-tsu''
*[[wiktionary:投|投]] throw ''tō'' or ''na-geru''
*[[wiktionary:拾|拾]] pick up ''shū'' or ''hiro-u''
*[[wiktionary:持|持]] hold ''ji'' or ''mo-tsu''
*[[wiktionary:指|指]] finger ''shi'' or ''yubi''
*[[wiktionary:放|放]] release ''hō'' or ''hana-su''
*[[wiktionary:整|整]] put in order ''sei'' or ''totono-eru''
*[[wiktionary:旅|旅]] trip ''ryo'' or ''ttabi''
*[[wiktionary:族|族]] tribe ''zoku''
*[[wiktionary:昔|昔]] long ago ''jaku'' or ''mukashi''
*[[wiktionary:昭|昭]] clear ''shō''
*[[wiktionary:暑|暑]] hot ''sho'' or ''atsu-i''
*[[wiktionary:暗|暗]] dark ''an'' or ''kura-i''
*[[wiktionary:曲|曲]] music or curve ''kyoku''
*[[wiktionary:有|有]] be ''yū'' or ''a-ru''
*[[wiktionary:服|服]] clothes ''fuku''
*[[wiktionary:期|期]] period of time ''ki'' or ''go''
*[[wiktionary:板|板]] board ''han'' or ''ita''
*[[wiktionary:柱|柱]] pillar ''chū'' or ''hashira''
*[[wiktionary:根|根]] root ''kon'' or ''ne''
*[[wiktionary:植|植]] plant ''shoku'' or ''u-eru''
*[[wiktionary:業|業]] business ''gyō'' or ''gō'' or ''waza''
*[[wiktionary:様|様]] appearance or Mr(Mrs,Ms) ''yō'' or ''sama''
*[[wiktionary:横|横]] side ''ō'' or ''yoko''
*[[wiktionary:橋|橋]] bridge ''kyō'' or ''hashi''
*[[wiktionary:次|次]] next ''ji'' or ''tsugi''
*[[wiktionary:歯|歯]] tooth ''shi'' or ''ha''
*[[wiktionary:死|死]] death ''shi''
*[[wiktionary:氷|氷]] ice ''hyō'' or ''kōri''
*[[wiktionary:決|決]] decide ''ketsu'' or ''ki-meru''
*[[wiktionary:油|油]] oil ''yu'' or ''abura''
*[[wiktionary:波|波]] wave ''ha'' or ''nami''
*[[wiktionary:注|注]] pour ''chū'' or ''soso-gu''
*[[wiktionary:泳|泳]] swim ''ei'' or ''oyo-gu''
*[[wiktionary:洋|洋]] ocean, western ''yō''
*[[wiktionary:流|流]] stream ''ryū'' or ''naga-reru''
*[[wiktionary:消|消]] extinguish ''shō'' or ''ke-su''
*[[wiktionary:深|深]] deep ''shin'' or ''fuka-i''
*[[wiktionary:温|温]] warm ''on'' or ''atata-kai''
*[[wiktionary:港|港]] harbor ''kō'' or ''minato''
*[[wiktionary:湖|湖]] lake ''ko'' or ''mizuumi''
*[[wiktionary:湯|湯]] hot water ''tō'' or ''yu''
*[[wiktionary:漢|漢]] China ''kan''
*[[wiktionary:炭|炭]] charcoal ''tan'' or ''sumi''
*[[wiktionary:物|物]] thing ''butsu'' or ''mono''
*[[wiktionary:球|球]] ball ''kyū'' or ''tama''
*[[wiktionary:由|由]] reason ''yū''
*[[wiktionary:申|申]] say ''shin'' or ''mō-su''
*[[wiktionary:界|界]] world ''kai''
*[[wiktionary:畑|畑]] agricultural field ''hatake''
*[[wiktionary:病|病]] sick ''byō'' or ''yamai''
*[[wiktionary:発|発]] departure ''hatsu''
*[[wiktionary:登|登]] climb ''to'' or ''nobo-ru''
*[[wiktionary:皮|皮]] skin ''hi'' or ''kawa''
*[[wiktionary:皿|皿]] dish ''sara''
*[[wiktionary:相|相]] mutual ''sō'' or ''ai''
*[[wiktionary:県|県]] prefecture ''ken''
*[[wiktionary:真|真]] true ''shin'' or ''ma''
*[[wiktionary:着|着]] wear ''chaku'' or ''ki-ru''
*[[wiktionary:短|短]] short ''tan'' or ''mijika-i''
*[[wiktionary:研|研]] sharpen ''ken'7 or ''to-gu''
*[[wiktionary:礼|礼]] thanks ''rei''
*[[wiktionary:神|神]] god(s) ''shin'' or ''kami''
*[[wiktionary:祭|祭]] festival ''sai'' or ''matsuri''
*[[wiktionary:福|福]] luck ''huku''
*[[wiktionary:秒|秒]] second ''byō''
*[[wiktionary:究|究]] research ''kyū'' or ''kiwa-meru''
*[[wiktionary:章|章]] chapter ''shō''
*[[wiktionary:童|童]] juvenile ''dō'' or ''warabe''
*[[wiktionary:笛|笛]] whistle ''teki'' or ''fue''
*[[wiktionary:第|第]] ordinal number prefix ''dai''
*[[wiktionary:筆|筆]] writing brush ''hitsu'' or ''fude''
*[[wiktionary:等|等]] class ''tō'' or ''nado''
*[[wiktionary:箱|箱]] box ''hako''
*[[wiktionary:級|級]] rank ''kyū''
*[[wiktionary:終|終]] end ''shū'' or ''owa-ru''
*[[wiktionary:緑|緑]] green ''ryoku'' or ''midori''
*[[wiktionary:練|練]] practice ''ren'' or ''ne-ru''
*[[wiktionary:羊|羊]] sheep ''yō'' or ''hitsuji''
*[[wiktionary:美|美]] beauty ''bi'' or ''utsuku-shii''
*[[wiktionary:習|習]] learn ''shū'' or ''nara-u''
*[[wiktionary:者|者]] someone ''sha'' or ''mono''
*[[wiktionary:育|育]] nurture ''iku'' or ''haguku-mu''
*[[wiktionary:苦|苦]] suffer ''ku'' or ''kuru-shii''
*[[wiktionary:荷|荷]] luggage ''ka'' or ''ni''
*[[wiktionary:落|落]] fall ''raku'' or ''o-chiru''
*[[wiktionary:葉|葉]] leaf ''yō'' or ''ha''
*[[wiktionary:薬|薬]] medicine ''yaku'' or ''kusuri''
*[[wiktionary:血|血]] blood ''ketsu'' or ''chi''
*[[wiktionary:表|表]] list or surface ''hyō'' or ''omote''
*[[wiktionary:詩|詩]] poem ''shi''
*[[wiktionary:調|調]] investigate ''chō'' or ''shira-beru''
*[[wiktionary:談|談]] discuss ''dan''
*[[wiktionary:豆|豆]] beans ''mame''
*[[wiktionary:負|負]] lose ''fu'' or ''ma-keru''
*[[wiktionary:起|起]] wake up ''ki'' or ''o-kiru''
*[[wiktionary:路|路]] road ''ro'' or ''michi''
*[[wiktionary:身|身]] body ''shin'' or ''mi''
*[[wiktionary:転|転]] revolve ''ten'' or ''koro-bu''
*[[wiktionary:軽|軽]] light ''kei'' or ''karu-i''
*[[wiktionary:農|農]] farming ''nō''
*[[wiktionary:返|返]] return ''hen'' or ''kae-su''
*[[wiktionary:追|追]] follow ''tsui'' or ''o-u''
*[[wiktionary:送|送]] send ''sō'' or ''oku-ru''
*[[wiktionary:速|速]] fast ''soku'' or ''haya-i''
*[[wiktionary:進|進]] advance ''shin'' or ''susu-mu''
*[[wiktionary:遊|遊]] play ''yū'' or ''aso-bu''
*[[wiktionary:運|運]] carry ''un'' or ''hako-bu''
*[[wiktionary:部|部]] part ''bu''
*[[wiktionary:都|都]] metropolis ''to'' or ''miyako''
*[[wiktionary:配|配]] distribute ''hai'' or ''kuba-ru''
*[[wiktionary:酒|酒]] alcoholic drink ''shu'' or ''sake''
*[[wiktionary:重|重]] heavy ''jū'' or ''omo-i''
*[[wiktionary:鉄|鉄]] iron ''tetsu''
*[[wiktionary:銀|銀]] silver ''gin''
*[[wiktionary:開|開]] open ''kai'' or ''hira-ku''
*[[wiktionary:院|院]] institution ''in''
*[[wiktionary:陽|陽]] sunshine ''hi'' or ''yō''
*[[wiktionary:階|階]] floor of a building ''kai''
*[[wiktionary:集|集]] collect ''shū'' or ''atsu-maru''
*[[wiktionary:面|面]] face ''men'' or ''tsura'' or ''omo'' or ''omote''
*[[wiktionary:題|題]] topic ''dai''
*[[wiktionary:飲|飲]] drink ''in'' or ''no-mu''
*[[wiktionary:館|館]] public building ''kan'' or ''yakata''
*[[wiktionary:駅|駅]] station ''eki''
*[[wiktionary:鼻|鼻]] nose ''bi'' or ''hana''

===Fourth grade (200 kanji)===
*[[wiktionary:不|不]] not ''hu''
*[[wiktionary:争|争]] conflict ''sō'' or ''araso-u''
*[[wiktionary:付|付]] attach ''hu'' or ''tsu-ku''
*[[wiktionary:令|令]] orders ''rei''
*[[wiktionary:以|以]] since ''i''
*[[wiktionary:仲|仲]] go-between ''naka''
*[[wiktionary:伝|伝]] transmit ''den'' or ''tsuta-eru''
*[[wiktionary:位|位]] rank ''i'' or ''kurai''
*[[wiktionary:低|低]] low ''tei'' or ''hiku-i''
*[[wiktionary:例|例]] example ''rei'' or ''tato-eru''
*[[wiktionary:便|便]] convenience ''ben'' or ''bin'' or ''tayo-ru''
*[[wiktionary:信|信]] trust ''shin'' or ''shin-jiru''
*[[wiktionary:倉|倉]] godown ''sō'' or ''kura''
*[[wiktionary:候|候]] climate ''kō''
*[[wiktionary:借|借]] borrow ''shaku'' or ''ka-riru''
*[[wiktionary:停|停]] halt ''tei'' or ''to-maru''
*[[wiktionary:健|健]] healthy ''ken'' or ''suko-yaka''
*[[wiktionary:側|側]] side ''soba'' or ''gawa''
*[[wiktionary:働|働]] work ''dō'' or ''hatara-ku''
*[[wiktionary:億|億]] hundred million ''oku''
*[[wiktionary:兆|兆]] portent　or trillion ''chō'' or ''kiza-shi''
*[[wiktionary:児|児]] child ''ji''
*[[wiktionary:共|共]] together ''kyō'' or ''tomo''
*[[wiktionary:兵|兵]] soldier ''hei'' or ''hyō'' or ''tsuwamono''
*[[wiktionary:典|典]] code ''ten''
*[[wiktionary:冷|冷]] cool ''rei'' or ''tsume-tai''
*[[wiktionary:初|初]] first ''sho'' or ''hatsu'' or ''ubu'' or ''ui'' or ''haji-mete''
*[[wiktionary:別|別]] separate ''betsu'' or ''waka-reru''
*[[wiktionary:利|利]] profit ''ri''
*[[wiktionary:刷|刷]] printing ''satsu'' or ''su-ru''
*[[wiktionary:副|副]] vice- ''huku''
*[[wiktionary:功|功]] achievement ''kō''
*[[wiktionary:加|加]] add ''ka'' or ''kuwa-eru''
*[[wiktionary:努|努]] toil ''do'' or ''tsuto-meru''
*[[wiktionary:労|労]] labor ''rō'' or ''negira-u''
*[[wiktionary:勇|勇]] courage ''yū'' or ''isa-mashii''
*[[wiktionary:包|包]] wrap ''hō'' or ''tsutu-mu''
*[[wiktionary:卒|卒]] graduate ''sotsu''
*[[wiktionary:協|協]] cooperation ''kyō''
*[[wiktionary:単|単]] simple ''tan''
*[[wiktionary:博|博]] Dr. ''haku''
*[[wiktionary:印|印]] mark ''in'' or ''shirushi''
*[[wiktionary:参|参]] participate or three ''san''
*[[wiktionary:史|史]] history ''shi''
*[[wiktionary:司|司]] director ''shi'' or ''tsukasado-ru''
*[[wiktionary:各|各]] each ''kaku''
*[[wiktionary:告|告]] tell ''koku'' or ''tsu-geru''
*[[wiktionary:周|周]] circumference ''shū''
*[[wiktionary:唱|唱]] chant ''shō'' or ''tona-eru''
*[[wiktionary:喜|喜]] rejoice ''ki'' or ''yoroko-bu''
*[[wiktionary:器|器]] container ''ki'' or ''utsuwa''
*[[wiktionary:囲|囲]] surround 'i' or ''kako-u''
*[[wiktionary:固|固]] harden ''ko'' or ''kata-maru''
*[[wiktionary:型|型]] model ''kei'' or ''kata''
*[[wiktionary:堂|堂]] public chamber ''dō''
*[[wiktionary:塩|塩]] salt ''shio''
*[[wiktionary:士|士]] gentleman ''shi''
*[[wiktionary:変|変]] change ''hen'' or ''ka-waru''
*[[wiktionary:央|央]] center ''ō''
*[[wiktionary:失|失]] lose ''sitsu'' or ''ushina-u''
*[[wiktionary:好|好]] like ''kō'' ''su-ku'' or ''kono-mu''
*[[wiktionary:季|季]] seasons ''ki''
*[[wiktionary:孫|孫]] grandson,granddaughtor ''son'' or ''mago''
*[[wiktionary:完|完]] perfect ''kan''
*[[wiktionary:官|官]] government official ''kan''
*[[wiktionary:害|害]] harm ''gai''
*[[wiktionary:察|察]] guess ''satsu''
*[[wiktionary:巣|巣]] nest ''sō'' or ''su''
*[[wiktionary:差|差]] distinction ''sa''
*[[wiktionary:希|希]] hope ''ki'' or ''mare''
*[[wiktionary:席|席]] seat ''seki''
*[[wiktionary:帯|帯]] sash ''tai'' or ''obi''
*[[wiktionary:底|底]] bottom ''tei'' or ''soko''
*[[wiktionary:府|府]] urban prefecture ''fu''
*[[wiktionary:康|康]] ease ''kō''
*[[wiktionary:建|建]] build ''ken'' or ''ta-teru''
*[[wiktionary:径|径]] diameter ''kei''
*[[wiktionary:徒|徒]] junior ''to''
*[[wiktionary:得|得]] acquire ''e-ru'' or ''toku''
*[[wiktionary:必|必]] without fail ''hitsu'' or ''kanara-zu''
*[[wiktionary:念|念]] thought ''nen''
*[[wiktionary:愛|愛]] love　''ai'' or ''ito-shii''
*[[wiktionary:成|成]] become ''sei'' or ''na-ru''
*[[wiktionary:戦|戦]] war ''sen'' or ''ikusa'' or ''tataka-u''
*[[wiktionary:折|折]] fold ''setsu'' or ''o-ru''
*[[wiktionary:挙|挙]] raise ''kyo'' or ''a-geru''
*[[wiktionary:改|改]] reformation ''kai'' or ''arata-meru''
*[[wiktionary:救|救]] salvation ''kyū'' or ''suku-u''
*[[wiktionary:敗|敗]] failure ''hai'' or ''yabur-reru''
*[[wiktionary:散|散]] scatter ''san'' or ''chi-ru''
*[[wiktionary:料|料]] fee ''ryō''
*[[wiktionary:旗|旗]] national flag ''hata''
*[[wiktionary:昨|昨]] previous ''saku''
*[[wiktionary:景|景]] scenery ''kei''
*[[wiktionary:最|最]] most ''sai'' or ''mo'' or ''motto-mo''
*[[wiktionary:望|望]] hope ''bō'' or ''nozo-mu''
*[[wiktionary:未|未]] un- ''mi'' or ''ima-da''
*[[wiktionary:末|末]] end ''matsu'' or ''sue''
*[[wiktionary:札|札]] tag ''satsu'' or ''huda''
*[[wiktionary:材|材]] lumber ''zai''
*[[wiktionary:束|束]] bundle ''soku'' or ''taba'' or ''tsuka''
*[[wiktionary:松|松]] pine ''shō'' or ''take''
*[[wiktionary:果|果]] fruit ''ka'' or ''ha-tasu''
*[[wiktionary:栄|栄]] prosperity ''ei'' or ''sakae-ru''
*[[wiktionary:案|案]] plan ''an''
*[[wiktionary:梅|梅]] plum ''bai'' or ''ume''
*[[wiktionary:械|械]] contraption ''kai''
*[[wiktionary:極|極]] poles ''kyoku'' or ''kiwa-meru''
*[[wiktionary:標|標]] signpost ''hyō''
*[[wiktionary:機|機]] machine ''ki''
*[[wiktionary:欠|欠]] lack ''ketsu'' or ''ka-keru''
*[[wiktionary:歴|歴]] curriculum ''reki''
*[[wiktionary:残|残]] remainder ''zan'' or ''noko-ru''
*[[wiktionary:殺|殺]] kill ''satsu'' or ''koro-su''
*[[wiktionary:毒|毒]] poison ''doku''
*[[wiktionary:氏|氏]] family name ''shi'' or ''uji''
*[[wiktionary:民|民]] people ''min'' or ''tami''
*[[wiktionary:求|求]] request ''kyu'' or ''moto-mu''
*[[wiktionary:治|治]] govern ''chi'' or ''osa-meru''
*[[wiktionary:法|法]] method ''hō''
*[[wiktionary:泣|泣]] cry ''kyū'' or ''na-ku''
*[[wiktionary:浅|浅]] shallow ''sen'' or ''asa-i''
*[[wiktionary:浴|浴]] bathe ''yoku'' or ''abi-ru''
*[[wiktionary:清|清]] pure ''sei'' or ''kiyo-raka''
*[[wiktionary:満|満]] full ''man'' or ''mi-chiru''
*[[wiktionary:漁|漁]] fishing ''ryō'' or ''asa-ru''
*[[wiktionary:灯|灯]] lamp ''tō'' or ''tomo-su''
*[[wiktionary:無|無]] nothing ''mu'' or ''na-i''
*[[wiktionary:然|然]] so ''zen'' or ''shika-shi''
*[[wiktionary:焼|焼]] bake ''shō'' or ''ya-ku''
*[[wiktionary:照|照]] illuminate ''sho'' or ''te-rasu''
*[[wiktionary:熱|熱]] heat ''netsu'' or ''atsu-i''
*[[wiktionary:牧|牧]] breed ''boku'' or ''maki''
*[[wiktionary:特|特]] special ''toku''
*[[wiktionary:産|産]] give birth ''san'' or ''u-mu''
*[[wiktionary:的|的]] target ''teki'' or ''mato''
*[[wiktionary:省|省]] government ministry ''sho'' or ''sei'' or ''habu-ku''
*[[wiktionary:祝|祝]] celebrate ''shuku'' or ''iwa-u''
*[[wiktionary:票|票]] ballot ''hyō''
*[[wiktionary:種|種]] kind or seed ''shu'' or ''tane'' or ''kusa''
*[[wiktionary:積|積]] accumulate ''seki'' or ''tsu-mu''
*[[wiktionary:競|競]] emulate ''kyō'' or ''kiso-u''
*[[wiktionary:笑|笑]] laugh ''shō'' or ''wara-u''
*[[wiktionary:管|管]] pipe ''kan'' or ''kuda''
*[[wiktionary:節|節]] node ''setsu'' or ''fushi''
*[[wiktionary:粉|粉]] flour ''ko'' or ''kona''
*[[wiktionary:紀|紀]] chronicle ''ki''
*[[wiktionary:約|約]] promise ''yaku''
*[[wiktionary:結|結]] tie ''ketsu'' or ''musu-bu'' or ''yu-u''
*[[wiktionary:給|給]] salary ''kyū'' or ''tama-u''
*[[wiktionary:続|続]] continue ''zoku'' or ''tsudu-ku''
*[[wiktionary:置|置]] put ''chi'' or ''o-ku''
*[[wiktionary:老|老]] old man ''rō'' or ''o-iru''
*[[wiktionary:胃|胃]] stomach ''i''
*[[wiktionary:脈|脈]] vein ''myaku''
*[[wiktionary:腸|腸]] intestines ''chō''
*[[wiktionary:臣|臣]] retainer ''shin''
*[[wiktionary:航|航]] cruise ''kō''
*[[wiktionary:良|良]] good ''ryō'' or ''yo-i''
*[[wiktionary:芸|芸]] art ''gei''
*[[wiktionary:芽|芽]] bud ''ga'' or ''me''
*[[wiktionary:英|英]] England ''ei''
*[[wiktionary:菜|菜]] vegetable ''na''
*[[wiktionary:街|街]] city ''gai'' or ''machi''
*[[wiktionary:衣|衣]] clothes ''i'' or ''koromo''
*[[wiktionary:要|要]] need ''yō'' or ''i-ru''
*[[wiktionary:覚|覚]] memorize ''kaku'' or ''sa-meru''
*[[wiktionary:観|観]] observe ''kan'' or ''mi-ru''
*[[wiktionary:訓|訓]] instruction ''kun''
*[[wiktionary:試|試]] test ''shi'' or ''kokoromi-ru''
*[[wiktionary:説|説]] theory ''setsu'' or ''to-ku''
*[[wiktionary:課|課]] section ''ka''
*[[wiktionary:議|議]] deliberation ''gi''
*[[wiktionary:象|象]] elephant ''zō'' or ''shō''
*[[wiktionary:貨|貨]] freight ''ka''
*[[wiktionary:貯|貯]] savings ''cho'' or ''ta-meru''
*[[wiktionary:費|費]] expense ''hi'' or ''tsui-yasu''
*[[wiktionary:賞|賞]] prize ''shō''
*[[wiktionary:軍|軍]] army ''gun''
*[[wiktionary:輪|輪]] wheel ''rin'' or ''wa''
*[[wiktionary:辞|辞]] resign ''ji'' or ''ya-meru''
*[[wiktionary:辺|辺]] environs ''hen'' or ''ata-ri''
*[[wiktionary:連|連]] take along ''ren'' or ''tsu-reru'' or ''tsura-neru''
*[[wiktionary:達|達]] attain ''tachi''
*[[wiktionary:選|選]] choose ''sen'' or ''era-bu''
*[[wiktionary:郡|郡]] county ''gun''
*[[wiktionary:量|量]] quantity ''ryō''
*[[wiktionary:録|録]] record ''roku''
*[[wiktionary:鏡|鏡]] mirror ''kyō'' or ''kagami''
*[[wiktionary:関|関]] related ''kan''
*[[wiktionary:陸|陸]] land ''riku''
*[[wiktionary:隊|隊]] group ''tai''
*[[wiktionary:静|静]] quiet ''sei'' or ''shizu-ka''
*[[wiktionary:順|順]] obey ''jun''
*[[wiktionary:願|願]] request ''gan'' or ''nega-u''
*[[wiktionary:類|類]] sort ''rui''
*[[wiktionary:飛|飛]] fly ''hi'' or ''to-bu''
*[[wiktionary:飯|飯]] meal ''han'' or ''meshi''
*[[wiktionary:養|養]] foster ''yō'' or ''yashina-u''
*[[wiktionary:験|験]] test ''ken''

===Fifth grade (185 kanji)===
*[[wiktionary:久|久]] long time ''kyū'' or ''hisa''
*[[wiktionary:仏|仏]] Buddha ''hutsu'' or ''butsu'' or ''hotoke''
*[[wiktionary:仮|仮]] sham ''kari''
*[[wiktionary:件|件]] affair ''ken''
*[[wiktionary:任|任]] responsibility ''nin'' or ''maka-seru''
*[[wiktionary:似|似]] becoming ''ji'' or ''ni-ru''
*[[wiktionary:余|余]] too much ''yo'' or ''ama-ru''
*[[wiktionary:価|価]] value ''ka''
*[[wiktionary:保|保]] preserve ''ho'' or ''tamo-tsu''
*[[wiktionary:修|修]] discipline ''shū'' or ''osa-meru''
*[[wiktionary:俵|俵]] straw bag ''hyō'' or ''tawara''
*[[wiktionary:個|個]] individual ''ko''
*[[wiktionary:備|備]] provide ''bi'' or ''sona-eru''
*[[wiktionary:像|像]] statue ''zō''
*[[wiktionary:再|再]] again ''sai'' or ''futata-bi''
*[[wiktionary:刊|刊]] publish ''kan''
*[[wiktionary:判|判]] judge ''han'' or ''waka-ru''
*[[wiktionary:制|制]] control ''sei''
*[[wiktionary:券|券]] ticket ''ken''
*[[wiktionary:則|則]] rule ''soku'' or ''notto-ru''
*[[wiktionary:効|効]] effect ''kō''
*[[wiktionary:務|務]] duty ''mu'' or ''tsuto-meru''
*[[wiktionary:勢|勢]] power ''sei'' or ''ikio-i''
*[[wiktionary:厚|厚]] thick ''kō'' or ''atsu-i''
*[[wiktionary:句|句]] phrase ''ku''
*[[wiktionary:可|可]] possible ''ka''
*[[wiktionary:営|営]] manage ''ei'' or ''itona-mu''
*[[wiktionary:因|因]] cause ''in'' or ''yo-ru''
*[[wiktionary:団|団]] group ''dan''
*[[wiktionary:圧|圧]] pressure ''atsu''
*[[wiktionary:在|在]] exist ''zai'' or ''a-ru''
*[[wiktionary:均|均]] level ''kin''
*[[wiktionary:基|基]] foundation ''ki'' or ''moto-duku''
*[[wiktionary:報|報]] report ''hō'' or ''muku-iru''
*[[wiktionary:境|境]] boundary ''kyō'' or ''sakai''
*[[wiktionary:墓|墓]] grave ''bo'' or ''haka''
*[[wiktionary:増|増]] increase ''zō'' or ''ma-su'' or ''fu-eru''
*[[wiktionary:夢|夢]] dream ''mu'' or ''yume''
*[[wiktionary:妻|妻]] wife ''sai'' or ''tsuma''
*[[wiktionary:婦|婦]] lady ''fu''
*[[wiktionary:容|容]] contain ''yō''
*[[wiktionary:寄|寄]] approach ''ki'' or ''yo-ru''
*[[wiktionary:富|富]] rich ''fu'' or ''tomi''
*[[wiktionary:導|導]] guide ''dō'' or ''michibi-ku''
*[[wiktionary:居|居]] reside ''kyo'' or ''i-ru''
*[[wiktionary:属|属]] belong ''zoku''
*[[wiktionary:布|布]] linen ''fu'' or ''nuno''
*[[wiktionary:師|師]] expert ''shi''
*[[wiktionary:常|常]] normal ''jō'' or ''tsune''
*[[wiktionary:幹|幹]] tree-trunk ''kan'' or ''miki''
*[[wiktionary:序|序]] preface ''jo''
*[[wiktionary:弁|弁]] valve ''ben''
*[[wiktionary:張|張]] stretch ''chō'' or ''ha-ru''
*[[wiktionary:往|往]] journey ''ō''
*[[wiktionary:復|復]] repeating ''fuku''
*[[wiktionary:徳|徳]] virtue ''toku''
*[[wiktionary:志|志]] intention ''shi'' or ''kokorozashi''
*[[wiktionary:応|応]] respond ''ō'' or ''kota-eru''
*[[wiktionary:快|快]] cheerful ''kai'' or '' kokoroyo-i''
*[[wiktionary:性|性]] gender ''sei'' or ''shō'' or ''saga''
*[[wiktionary:恩|恩]] grace ''on''
*[[wiktionary:情|情]] feelings ''jō'' or ''nasa-ke''
*[[wiktionary:態|態]] condition ''tai''
*[[wiktionary:慣|慣]] accustomed ''kan'' or ''na-reru''
*[[wiktionary:承|承]] acquiesce ''shō'' or ''uketamawa-ru''
*[[wiktionary:技|技]] skill ''gi'' or ''waza''
*[[wiktionary:招|招]] beckon ''shō'' or ''mane-ku''
*[[wiktionary:授|授]] instruct ''ju'' or ''sazu-keru''
*[[wiktionary:採|採]] pick ''sai'' or ''to-ru''
*[[wiktionary:接|接]] contact ''setsu''
*[[wiktionary:提|提]] present ''tei'' or ''sa-geru''
*[[wiktionary:損|損]] loss ''son'' or ''soko-neru''
*[[wiktionary:支|支]] branch ''shi'' or ''sasa-eru''
*[[wiktionary:政|政]] politics ''sei'' or ''matsurigoto''
*[[wiktionary:故|故]] circumstances ''ko'' or ''yue''
*[[wiktionary:敵|敵]] enemy ''teki'' or ''kataki''
*[[wiktionary:断|断]] cut off ''dan'' or ''ta-tsu''
*[[wiktionary:旧|旧]] old times ''kyū''
*[[wiktionary:易|易]] easy ''eki'' or ''yasa-shii''
*[[wiktionary:暴|暴]] outburst ''bō'' or ''aba-ku''
*[[wiktionary:条|条]] clause ''jō''
*[[wiktionary:枝|枝]] branch ''shi'' or ''eda''
*[[wiktionary:査|査]] investigate ''sa''
*[[wiktionary:格|格]] status ''kaku''
*[[wiktionary:桜|桜]] cherry ''ō'' or ''sakura''
*[[wiktionary:検|検]] examine ''ken''
*[[wiktionary:構|構]] construct ''kō'' or ''kama-eru''
*[[wiktionary:武|武]] military ''bu''
*[[wiktionary:比|比]] compare ''hi'' or ''kura-beru''
*[[wiktionary:永|永]] eternity ''ei'' or ''naga-i''
*[[wiktionary:河|河]] river ''ga'' or ''kawa''
*[[wiktionary:液|液]] fluid ''eki''
*[[wiktionary:混|混]] mix ''kon'' or ''maza-ru''
*[[wiktionary:減|減]] decrease ''gen'' or ''he-ru''
*[[wiktionary:測|測]] fathom ''soku'' or ''haka-ru''
*[[wiktionary:準|準]] standard ''jun''
*[[wiktionary:演|演]] perform ''en''
*[[wiktionary:潔|潔]] undefiled ''ketsu'' or ''isagiyo-i''
*[[wiktionary:災|災]] disaster ''sai'' or ''wazawa-i''
*[[wiktionary:燃|燃]] burn ''nen'' or ''mo-eru''
*[[wiktionary:版|版]] printing block ''han''
*[[wiktionary:犯|犯]] crime ''han'' or ''oka-su''
*[[wiktionary:状|状]] form ''jō''
*[[wiktionary:独|独]] alone ''doku'' or ''hito-ri''
*[[wiktionary:率|率]] rate ''ritsu'' or ''hikii-ru''
*[[wiktionary:現|現]] appear ''gen'' or ''arawa-reru''
*[[wiktionary:留|留]] detain ''ryū'' ''ru'' or ''todo-maru''
*[[wiktionary:略|略]] abbreviation ''ryaku''
*[[wiktionary:益|益]] benefit ''eki'' or ''ma-su''
*[[wiktionary:眼|眼]] eyeball ''gan'' or ''me''
*[[wiktionary:破|破]] rend ''ha'' or ''yabu-ru''
*[[wiktionary:確|確]] certain ''kaku'' or ''tashi-ka''
*[[wiktionary:示|示]] indicate ''shi'' or ''shime-su''
*[[wiktionary:祖|祖]] ancestor ''so''
*[[wiktionary:禁|禁]] prohibition ''kin''
*[[wiktionary:移|移]] shift ''i'' or ''utsu-ru''
*[[wiktionary:程|程]] extent ''tei'' or ''hodo''
*[[wiktionary:税|税]] tax ''zei''
*[[wiktionary:築|築]] fabricate ''chiku'' or ''kizu-ku''
*[[wiktionary:精|精]] refined ''sei''
*[[wiktionary:素|素]] elementary ''su'' or ''moto''
*[[wiktionary:経|経]] manage ''kei'' ''he-ru''
*[[wiktionary:統|統]] unite ''tō'' or ''su-beru''
*[[wiktionary:絶|絶]] discontinue ''zetsu'' or ''ta-tsu''
*[[wiktionary:綿|綿]] cotton ''men'' or ''wata''
*[[wiktionary:総|総]] whole ''sō''
*[[wiktionary:編|編]] compile ''hen'' or ''a-mu''
*[[wiktionary:績|績]] exploits ''seki''
*[[wiktionary:織|織]] weave ''shiki'' or ''o-ru''
*[[wiktionary:罪|罪]] guilt ''zai'' or ''tsumi''
*[[wiktionary:群|群]] flock ''gun'' ''mu-reru''
*[[wiktionary:義|義]] righteousness ''gi''
*[[wiktionary:耕|耕]] till ''kō'' or ''tagaya-su''
*[[wiktionary:職|職]] employment ''shoku''
*[[wiktionary:肥|肥]] fertilizer ''hi'' or ''ko-yasu''
*[[wiktionary:能|能]] ability ''nō''
*[[wiktionary:興|興]] entertain ''kyō'' or ''oko-su''
*[[wiktionary:舌|舌]] tongue ''zetsu'' or ''shita''
*[[wiktionary:舎|舎]] cottage ''sha''
*[[wiktionary:術|術]] art ''jutsu'' or ''sube''
*[[wiktionary:衛|衛]] defense ''ei''
*[[wiktionary:製|製]] manufacture ''sei''
*[[wiktionary:複|複]] duplicate ''fuku''
*[[wiktionary:規|規]] rule ''ki''
*[[wiktionary:解|解]] untie ''ge'' or ''kai'' or ''to-ku''
*[[wiktionary:設|設]] establish ''setsu'' or ''mouke-ru''
*[[wiktionary:許|許]] permit ''kyo'' or ''yuru-su''
*[[wiktionary:証|証]] evidence ''shō''
*[[wiktionary:評|評]] evaluate ''hyō''
*[[wiktionary:講|講]] lecture ''kō''
*[[wiktionary:謝|謝]] apologize ''sha'' or ''ayama-ru''
*[[wiktionary:識|識]] discriminating ''shiki''
*[[wiktionary:護|護]] safeguard ''go'' or ''mamo-ru''
*[[wiktionary:豊|豊]] bountiful ''hō'' or ''yuta-ka''
*[[wiktionary:財|財]] wealth ''zai''
*[[wiktionary:貧|貧]] poor ''hin'' or ''mazushi-i''
*[[wiktionary:責|責]] blame ''seki'' or ''se-meru''
*[[wiktionary:貸|貸]] lend ''tai'' or ''ka-su''
*[[wiktionary:貿|貿]] trade ''bō''
*[[wiktionary:賀|賀]] congratulations ''ga''
*[[wiktionary:資|資]] resources ''shi''
*[[wiktionary:賛|賛]] approve ''san''
*[[wiktionary:質|質]] quality ''shitsu''
*[[wiktionary:輸|輸]] transport ''yu''
*[[wiktionary:述|述]] mention ''jutsu'' or ''no-beru''
*[[wiktionary:迷|迷]] astray ''mei'' or ''mayo-u''
*[[wiktionary:退|退]] retreat ''tai'' or ''shirizo-ku'' or ''do-ku'' or ''no-ku''
*[[wiktionary:逆|逆]] inverted ''gyaku'' or ''sakara-u''
*[[wiktionary:造|造]] create ''zō'' or ''tsuku-ru''
*[[wiktionary:過|過]] go beyond ''ka'' or ''ayama-chi''
*[[wiktionary:適|適]] suitable ''teki''
*[[wiktionary:酸|酸]] acid ''san''
*[[wiktionary:鉱|鉱]] mineral ''kō''
*[[wiktionary:銅|銅]] copper ''dō''
*[[wiktionary:銭|銭]] coin ''sen'' or ''zeni''
*[[wiktionary:防|防]] prevent ''bō'' or ''fuse-gu''
*[[wiktionary:限|限]] limit ''gen'' or ''kagi-ru''
*[[wiktionary:険|険]] precipitous ''ken''
*[[wiktionary:際|際]] occasion ''sai'' or ''kiwa''
*[[wiktionary:雑|雑]] miscellaneous ''zatsu''
*[[wiktionary:非|非]] negative ''hi'' or ''ara-zu''
*[[wiktionary:預|預]] deposit ''yo'' or ''azu-keru''
*[[wiktionary:領|領]] territory ''ryō''
*[[wiktionary:額|額]] amount ''gaku'' or ''hitai''
*[[wiktionary:飼|飼]] domesticate ''shi'' or ''ka-u''

===Sixth grade (181 kanji)===
*[[wiktionary:並|並]] row ''hei'' or 'nami'' or ''nara-bu''
*[[wiktionary:乱|乱]] riot ''ran'' or ''mida-reru''
*[[wiktionary:乳|乳]] milk ''nyū'' or ''chichi''
*[[wiktionary:亡|亡]] deceased ''bō'' or ''na-kunaru''
*[[wiktionary:仁|仁]] kindness ''jin''
*[[wiktionary:供|供]] offer ''kyō'' or ''ku'' or ''tomo'' or ''sona-eru''
*[[wiktionary:俳|俳]] actor ''hai''
*[[wiktionary:値|値]] value ''chi'' or ''atai''
*[[wiktionary:傷|傷]] wound ''shō'' or ''kizu''
*[[wiktionary:優|優]] superior ''yū'' or ''yasa-shii''
*[[wiktionary:党|党]] political party ''tō''
*[[wiktionary:冊|冊]] counter for books ''satsu''
*[[wiktionary:処|処]] dispose ''sho''
*[[wiktionary:刻|刻]] engrave ''koku'' or ''kiza-mu''
*[[wiktionary:割|割]] divide ''katsu'' or ''wa-ru''
*[[wiktionary:創|創]] create ''sō'' or ''tsuku-ru''
*[[wiktionary:劇|劇]] drama ''geki''
*[[wiktionary:勤|勤]] diligence ''kin'' or ''tsuto-meru''
*[[wiktionary:危|危]] dangerous ''ki'' or ''aya-ui''
*[[wiktionary:卵|卵]] egg ''ran'' or ''tamago''
*[[wiktionary:厳|厳]] strict ''gen'' or ''kibi-shii''
*[[wiktionary:収|収]] take in ''shū'' or ''osa-meru''
*[[wiktionary:后|后]] queen ''gō'' or ''kisaki''
*[[wiktionary:否|否]] negate ''hi'' or ''ina'' or ''iya''
*[[wiktionary:吸|吸]] suck ''kyū'' or ''su-u''
*[[wiktionary:呼|呼]] call ''ko'' or ''yo-bu''
*[[wiktionary:善|善]] good ''zen'' or ''yo-i''
*[[wiktionary:困|困]] become distressed ''kon'' or ''koma-ru''
*[[wiktionary:垂|垂]] droop ''choku'' or ''ta-reru''
*[[wiktionary:城|城]] castle ''jō'' or ''shiro''
*[[wiktionary:域|域]] range ''iki''
*[[wiktionary:奏|奏]] play music ''sō'' or ''kana-deru''
*[[wiktionary:奮|奮]] stirred up ''hun'' or ''huru-u''
*[[wiktionary:姿|姿]] shape ''shi'' or ''sugata''
*[[wiktionary:存|存]] suppose ''son''
*[[wiktionary:孝|孝]] filial piety ''kō''
*[[wiktionary:宅|宅]] home ''taku''
*[[wiktionary:宇|宇]] eaves ''u''
*[[wiktionary:宗|宗]] religion ''shū'' or ''sō''
*[[wiktionary:宙|宙]] mid-air ''chū''
*[[wiktionary:宝|宝]] treasure ''hō'' or ''takara''
*[[wiktionary:宣|宣]] proclaim ''sen'' or ''notama-u''
*[[wiktionary:密|密]] secrecy ''mitsu''
*[[wiktionary:寸|寸]] measurement ''sun''
*[[wiktionary:専|専]] specialty ''sen'' or ''moppa-ra''
*[[wiktionary:射|射]] shoot ''sha'' or ''i-ru''
*[[wiktionary:将|将]] leader ''shō''
*[[wiktionary:尊|尊]] revered ''son''
*[[wiktionary:就|就]] concerning ''shū'' or ''tsu-ku''
*[[wiktionary:尺|尺]] measure of length ''shaku''
*[[wiktionary:届|届]] deliver ''todo-ku''
*[[wiktionary:展|展]] expand ''ten''
*[[wiktionary:層|層]] stratum ''sō''
*[[wiktionary:己|己]] self ''ko'' or ''onore''
*[[wiktionary:巻|巻]] scroll ''kan'' or ''ma-ku''
*[[wiktionary:幕|幕]] curtain ''baku'' or ''maku''
*[[wiktionary:干|干]] dry ''kan'' or ''ho-su''
*[[wiktionary:幼|幼]] infancy ''yō'' or ''osana-i''
*[[wiktionary:庁|庁]] government office ''chō''
*[[wiktionary:座|座]] sit ''za'' or ''suwa-ru''
*[[wiktionary:延|延]] prolong ''en'' or ''no-basu''
*[[wiktionary:律|律]] rhythm ''ritsu''
*[[wiktionary:従|従]] obey ''jun'' or ''sitaga-u''
*[[wiktionary:忘|忘]] forget ''bō'' or ''wasu-reru''
*[[wiktionary:忠|忠]] loyalty ''chū''
*[[wiktionary:憲|憲]] constitution ''ken''
*[[wiktionary:我|我]] ego ''ga'' or ''ware''
*[[wiktionary:批|批]] criticism ''hi''
*[[wiktionary:担|担]] shouldering ''tan'' or ''nina-u''
*[[wiktionary:拝|拝]] worship ''hai'' or ''oga-mu''
*[[wiktionary:拡|拡]] broaden ''kaku'' or ''hiro-geru''
*[[wiktionary:捨|捨]] throw away ''sha'' or ''su-teru''
*[[wiktionary:探|探]] grope ''tan'' or ''saga-su''
*[[wiktionary:推|推]] infer ''sui''
*[[wiktionary:揮|揮]] command ''ki''
*[[wiktionary:操|操]] maneuver ''sō'' or ''ayatsu-ru''
*[[wiktionary:敬|敬]] respect ''kei'' or ''uyama-u''
*[[wiktionary:映|映]] reflect ''ei'' or ''utsu-ru''
*[[wiktionary:晩|晩]] nightfall ''ban''
*[[wiktionary:暖|暖]] warmth ''dan'' or ''atata-kai''
*[[wiktionary:暮|暮]] livelihood ''bo'' or ''ku-rasu''
*[[wiktionary:朗|朗]] melodious ''rō'' or ''hoga-raka''
*[[wiktionary:机|机]] desk ''ki'' or ''tsukue''
*[[wiktionary:枚|枚]] sheet of... ''mai''
*[[wiktionary:染|染]] dye ''sen'' or ''so-meru''
*[[wiktionary:株|株]] stocks ''kabu''
*[[wiktionary:棒|棒]] rod ''bō''
*[[wiktionary:模|模]] imitation ''mo''
*[[wiktionary:権|権]] rights ''ken''
*[[wiktionary:樹|樹]] trees ''ju'' or ''ki''
*[[wiktionary:欲|欲]] longing ''yoku'' or ''ho-shii''
*[[wiktionary:段|段]] steps ''dan''
*[[wiktionary:沿|沿]] run alongside ''en'' or ''so-u''
*[[wiktionary:泉|泉]] fountain ''sen'' or ''izumi''
*[[wiktionary:洗|洗]] wash ''sen'' or ''ara-u''
*[[wiktionary:派|派]] sect ''ha''
*[[wiktionary:済|済]] settle ''sai'' or ''su-mu''
*[[wiktionary:源|源]] origin ''gen'' or ''minamoto''
*[[wiktionary:潮|潮]] tide ''cho'' or ''shio''
*[[wiktionary:激|激]] violent ''geki'' or ''hage-shii''
*[[wiktionary:灰|灰]] ashes ''hai''
*[[wiktionary:熟|熟]] ripen ''juku'' or ''u-reru''
*[[wiktionary:片|片]] one-sided ''hen'' ore ''kata''
*[[wiktionary:班|班]] group ''han''
*[[wiktionary:異|異]] uncommon ''i'' or ''koto-naru''
*[[wiktionary:疑|疑]] doubt ''gi'' or ''utaga-u''
*[[wiktionary:痛|痛]] pain ''tsū'' or ''ita-i''
*[[wiktionary:皇|皇]] emperor ''kō'' or ''ō''
*[[wiktionary:盛|盛]] prosper ''sei'' or ''mo-ru''
*[[wiktionary:盟|盟]] alliance ''mei''
*[[wiktionary:看|看]] watch over ''kan''
*[[wiktionary:砂|砂]] sand ''sa'' or ''sha'' or ''suna''
*[[wiktionary:磁|磁]] magnet ''ji''
*[[wiktionary:私|私]] me ''shi'' or ''watakushi'' or ''watashi''
*[[wiktionary:秘|秘]] secret ''hi''
*[[wiktionary:穀|穀]] serial ''koku''
*[[wiktionary:穴|穴]] hole ''ketsu'' or ''ana''
*[[wiktionary:窓|窓]] window ''sō'' or ''mado''
*[[wiktionary:筋|筋]] muscle ''kin'' or ''suji''
*[[wiktionary:策|策]] scheme ''saku''
*[[wiktionary:簡|簡]] simplicity ''kan''
*[[wiktionary:糖|糖]] sugar ''tō''
*[[wiktionary:系|系]] lineage ''kei''
*[[wiktionary:紅|紅]] deep red ''kō'' or ''beni'' or ''kurenai''
*[[wiktionary:納|納]] settlement ''nō'' or ''osa-meru''
*[[wiktionary:純|純]] genuine ''jun''
*[[wiktionary:絹|絹]] silk ''ken'' or ''kinu''
*[[wiktionary:縦|縦]] vertical ''ju'' or ''tate''
*[[wiktionary:縮|縮]] shrink ''shuku'' or ''chidi-mu''
*[[wiktionary:署|署]] government office ''sho''
*[[wiktionary:翌|翌]] the following ''yoku''
*[[wiktionary:聖|聖]] holy ''sei''
*[[wiktionary:肺|肺]] lung ''hai''
*[[wiktionary:背|背]] back ''hai'' or ''se''
*[[wiktionary:胸|胸]] bosom ''kyō'' or ''mune''
*[[wiktionary:脳|脳]] brain ''nō''
*[[wiktionary:腹|腹]] abdomen ''fuku'' or ''hara''
*[[wiktionary:臓|臓]] entrails ''zō''
*[[wiktionary:臨|臨]] lookover ''rin'' or ''nozo-mu''
*[[wiktionary:至|至]] climax ''shi'' or ''ita-ru''
*[[wiktionary:若|若]] young ''jaku'' or ''waka-i''
*[[wiktionary:著|著]] renowned ''cho''
*[[wiktionary:蒸|蒸]] steam ''jō'' or ''mu-su''
*[[wiktionary:蔵|蔵]] warehouse ''zō'' or ''kura''
*[[wiktionary:蚕|蚕]] silkworm ''kaiko''
*[[wiktionary:衆|衆]] masses ''shū''
*[[wiktionary:裁|裁]] judge ''sai'' or ''saba-ku''
*[[wiktionary:装|装]] attire ''sō'' or ''shō'' or ''yosoo-u''
*[[wiktionary:裏|裏]] back ''ri'' or ''ura''
*[[wiktionary:補|補]] supplement ''ho'' or ''ogina-u''
*[[wiktionary:視|視]] look at ''shi'' or ''mi-ru''
*[[wiktionary:覧|覧]] perusal ''ran''
*[[wiktionary:討|討]] chastise ''tō'' or ''u-tsu''
*[[wiktionary:訪|訪]] visit ''hō'' or ''otozu-reru''
*[[wiktionary:訳|訳]] translate ''yaku'' or ''wake''
*[[wiktionary:詞|詞]] poetry ''shi'' or ''kotoba''
*[[wiktionary:誌|誌]] document ''shi''
*[[wiktionary:認|認]] recognize ''nin'' or ''mito-meru''
*[[wiktionary:誕|誕]] born ''tan''
*[[wiktionary:誠|誠]] sincerity ''sei'' or ''makoto''
*[[wiktionary:誤|誤]] mistake ''go'' or ''ayama-ru''
*[[wiktionary:論|論]] theory ''ron''
*[[wiktionary:諸|諸]] everything ''sho'' or ''moro''
*[[wiktionary:警|警]] guard against ''kei''
*[[wiktionary:貴|貴]] precious ''ki''
*[[wiktionary:賃|賃]] fare ''chin''
*[[wiktionary:遺|遺]] bequeath ''i''
*[[wiktionary:郵|郵]] mail ''yū''
*[[wiktionary:郷|郷]] home town ''kyō'' or ''gō''
*[[wiktionary:針|針]] needle ''shin'' or ''hari''
*[[wiktionary:鋼|鋼]] steel ''gō'' or ''hagane''
*[[wiktionary:閉|閉]] closed ''hei'' or ''shi-meru''
*[[wiktionary:閣|閣]] tall ''kaku''
*[[wiktionary:降|降]] descend ''kō'' or ''o-riru''
*[[wiktionary:陛|陛]] majesty ''hei''
*[[wiktionary:除|除]] exclude ''jo'' or ''nozo-ku''
*[[wiktionary:障|障]] hurt ''shō'' or ''sawa-ru''
*[[wiktionary:難|難]] difficult ''nan'' or ''muzuka-shii''
*[[wiktionary:革|革]] leather ''kaku'' or ''kawa''
*[[wiktionary:頂|頂]] place on the head ''chō'' or ''itada-ku''
*[[wiktionary:骨|骨]] bone ''kotsu'' or ''hone''

==See also==

*[[Learning kanji]]

[[Category:Kanji]]

[[fr:Kyôiku kanji]]
[[ja:教育漢字]]

Gay Nigger Association of America

2005-11-19T22:57:27Z

Simetrical: /* Notable trolls */ They didn't *claim* to create fakes

:''The Gay Nigger Association of America is most commonly known as the GNAA. For other uses of the [[acroynm]], see [[GNAA]]''.
[[Image:Gnaa-logo.png|thumb|The GNAA logo]]

The '''Gay Nigger Association of America''' (better known by its four letter abbreviation '''GNAA''') is a self-aggrandizing [[Internet troll]] [[troll organization|organization]] that primarily targets [[Internet]] communities in an effort to cause havoc and disrupt their normal activities. The GNAA designed their name to be [[offend|offensive]] and it is generally assumed to have been chosen because of the [[Social stigma|stigma]] that is associated with [[homosexuality]] and the impact of the [[List of ethnic slurs|racial slur]] "[[nigger]]". Although it is termed "Association of America" the organization also has participants from countries other than the [[United States of America]].

Members engage in such nefarious activities as flooding [[weblog]]s, producing [[shock sites]], [[prank call|prank-call]]ing [[technical support]] telephone lines, and [[Internet Relay Chat|IRC channel]] disruption such as [[IRC floods]]. Due to these actions the normal operation of many popular websites such as [[slashdot.org]] is interrupted, and sometimes the attacks force websites to shut down temporarily. As such, targeted communities generally consider GNAA members a [[nuisance]] and frequently respond with [[technology|technological]] and social anti-trolling measures such as [[moderation system]]s to limit future disruption caused by the trolling. The inner-workings of the GNAA are not well known, and some speculate that the GNAA consists solely of unconnected individuals acting in the name of the group.

==Background information==

The GNAA first appeared in [[January 2003]], trolling Slashdot using [[ASCII art]] [[logo|logos]] representing the organization and [[satire|satirical]] [[news release]]s pertaining to the contents of Slashdot articles. As with other troll organizations, members of the GNAA adopt [[pseudonym|pseudonyms]] to preserve their [[anonymity]] and their true identities are generally not known. While its number of members are unknown, the GNAA has listed members "timecop" as the founder and President and "jesuitx" as a co-founder and Vice President. The internal structure of the GNAA is unclear and some argue that they have no real structure or actual members; business is conducted in secret and those acting in its name may simply be individuals working under the GNAA "brand."

The GNAA's website features pictures of African American athletes and professionals that appear to originate from stock image archives in an apparent attempt to parody the designs of various corporate websites. It states that the GNAA does not either support or promote [[racism]], [[homophobia]], or other kinds of hatred. While their main motivations are difficult to determine, they claim to have targeted websites and blogs that promote "anti Gaynigger and pro-[[Zionist]] [[propaganda]]". {{ref|GNAAmotives}}


GNAA members Rucas and Armorfist created a [[shock site]] called [[List of shock sites#Last Measure|Last Measure]], which the GNAA often links or redirects to in their various activities. In order to automate their activities, the GNAA has created many programmatic scripts for uses such as [[crapflooding]] sites. The source code of these scripts are usually made available under the [[BSD license|revised BSD license]]. One such script is ASIAN, The Automated Synchronous [[IRC]] Assault Network, a clone of a popular [[IRC]] flooding tool called AYSYN (Are you stupid? Yes/No) by mef. It was created by member Rucas and abez due to the many bugs found in AYSYN and the lack of source code. It uses SOCKS proxies and [[tor]] to connect numerous drones to an [[IRC]] server and use them to flood various people and channels.

==Membership==

GNAA encourages people to join by suggesting that potential recruits watch the [[1992 in film|1992]] [[Denmark|Danish]] [[B-movie|low-budget movie]] ''[[Gayniggers From Outer Space]]'', from which their name derives. The GNAA's entry requirements also include successfully achieving a "[[first post]]" on Slashdot consisting of GNAA [[Internet troll|troll]] text or registering support by upward [[moderation]] of GNAA comments. A test on the subject matter in ''Gayniggers From Outer Space'' is then administered by an [[IRC bot]].

[[Image:GNAA ascii sig.png|thumb|250px|GNAA ASCII signature]]

The GNAA has a [[signature block|signature]] which their members use whenever they perform a [[crapflooding|crapflood]] or post a news release. The full "[[sig]]", which includes an embedded [[ASCII art]] picture of the letters "GNAA" on a wall, can be found on their website. It begins:

:GNAA (GAY NIGGER ASSOCIATION OF AMERICA) is the first organization which gathers GAY NIGGERS from all over America and abroad for one common goal - being GAY NIGGERS.

:*Are you GAY?
:*Are you a NIGGER?
:*Are you a GAY NIGGER?

:If you answered "Yes" to all of the above questions, then GNAA (GAY NIGGER ASSOCIATION OF AMERICA) might be exactly what you've been looking for!

The signature text is significant because it identifies a GNAA attack.

All the members of the GNAA act anonymously, though some pseudonyms have become known. One of the most oft-mentioned members in the GNAA is "Gary Niger", a play on the words "Gay Nigger". Gary, a fictional character coined by GNAA vice-president jesuitx, is cited as a press contact in most press releases the GNAA releases, and also frequently appears as the name in their trolling activities. Another member, "rolloffle", who has since left the GNAA, participated in many trolling incidents and created many scripts to cause problems for various software programs that are used in internet forums. "Rolloffle" was also the author of the article "Why your Movable Type blog must die", which was published on the website [[Kuro5hin]]. GNAA member "Rucas" is the lead developer of GNAA Last Measure and until recently hosted the largest Last Measure mirror at peoplesprimary.com. He has recently released ''latvianbotnet.pl'', a [[Perl]] script to [[crapflood]] [[IRC]] channels. GNAA member "[[l0de]]" was the head technician and host of his Internet radio show, the [[l0de Radio Hour]]. Broadcasts have been suspended following his alleged death in [[September]] of [[2005]], although this appears to be a hoax. {{ref|lode}} GNAA member Staos passed away in [[November]] of [[2005]] of Acute lymphocytic [[leukemia]].

==Activities==
[[Image:GNNA_crapflood.png|thumb|Attempt to crapflood Slashdot by the GNAA: note topics modded down to -1]]
===Disruption===
One of the aims of the GNAA is to cause disruption on the Internet. They tend to target community webboards blogs and have been moderately successful in disrupting both major and minor sites. They first gained notoriety in the [[Slashdot]] community when they launched several [[crapflooding|flood attacks]] against the site. Slashdot subsequently implemented [[open proxy]]-banning measures in its posting system; GNAA members claim that their crapflooding campaign spurred this change. They also registered many usernames ''en masse'' to mark a Slashdot editor who uses the name "michael" as their foe. {{ref|slashdot}} In late [[2004]], the GNAA discovered vulnerabilities in weblogging service [[Xanga]]. In a related attack, they launched a [[Denial of Service]] attack on Slashdot, taking down its [[search engine]] for a few days. {{ref|kuro5hin}} During [[May 2004]], GNAA members flooded the popular image board [[4chan]], contributing to the fourth non-permanent shutdown of the site shortly thereafter. In the list of reasons why it closed down, the administrator wrote: "Flooding. GNAA put the final nail in the coffin, however I am thankful that they willingly ceased the flood after finding out it was costing me money." However, a poster on the [[Something Awful Forums]] later stated that this was only one of several factors that caused them to be shut down: "It was not the GNAA who killed 4chan (I quite like them actually), or really the moronic users, it was a man named Chris, who goes by the name TheRowan and runs a business that shuts you down if you fail to play along." {{ref|somethingawful}} The GNAA cause more disruption on IRC as they are known to crapflood channels. Many IRC servers do not allow the GNAA channel to exist due to this disruption, for instance on Freenode's IRC server, the #GNAA channel redirects to #you_have_got_to_be_kidding with a warning message indicating that the network might be inappropriate. This is standard Freenode behavior for juped channels. Other IRC networks similarly jupe #GNAA.

===Notable trolls===
The two most notable trolls that the GNAA have performed involved Mac OS X users and Harry Potter readers. In [[July 2004]], GNAA members jesuitx and DivineTom submitted leaked [[screenshot]]s of the forthcoming [[operating system]] [[Mac OS X v10.4]] to the popular [[Apple Computer|Apple]] [[Apple Macintosh|Macintosh]] news website MacRumors, which read "With WWDC just days away, the first Tiger information and screenshots appears to have been leaked. According to sources, Apple will reportedly provide developers with a Mac OS X 10.4 Preview copy at WWDC on Monday. The screenshots provided reportedly come from this upcoming developer preview." {{ref|macrumors}} When people found out the source was the GNAA many declared the screenshots to be fake based on the organization's disreputability in the past. Later, the GNAA released a press release which claimed that the screenshots were genuine (cf. [http://www.apple.com/macosx/tiger/dashboard.html official Apple screenshots]), and that they trolled the Apple community. {{ref|appleinsider}}

[[Image:Dattebayo.jpg|thumb|Dattebayo fansub website with GNAA notice]]
In [[June 2005]], the GNAA claimed to have created a [[Mac OS X]] Tiger release for [[Intel x86]] processors which caught media attention from Mac Daily News [[June 11]]. {{ref|macdailynews}} The next day, the supposed leak made front page news on Slashdot and was mentioned on the [[G4 (television)|G4]] show ''[[Attack of the Show]]'' {{ref|gnauk}}. The DVD image released onto [[BitTorrent]] merely booted an image of hello.jpg ([[Goatse.cx|goatse]]) instead of the leaked operating system as some had thought, and the remaining several gigabytes of space on the DVD was filled with a repetition of the text "GNAAGNAA...". The same hoax was created again in [[August]] of 2005, this time with a fake bootloader that gave generic error messages if the date was before August the 4th, and after that date it displayed the content from the shock site "Last Measure" {{ref|gnauk}}

Upon the impending release of the next book in the [[Harry Potter]] series, ''[[Harry Potter and the Half-Blood Prince]]'', the GNAA claimed to have created a [[PDF]] file of the book, which contained various [[shock images]] and released it to [[BitTorrent]]. In addition, the GNAA also posted various spoilers about the new book onto a Harry Potter fan [[forum]] which caused them to temporarily shut down until 1-2 days after the book's release, and a GNAA member by the name of Zeikfried also created a website a few days before the release of the book on which various [[plot]] [[spoilers]] of the book were disseminated . {{ref|gnauk}}

Several other notable incidents involved trolling anime fans and Dremel website administrators. In [[August]] 2005, the GNAA released a copy of [[Gayniggers from Outer Space]] onto the [[fansub]] website [[Dattebayo]], which was falsely labeled as episode 146 of the Japanese anime show ''[[Naruto (manga)|Naruto]]''. The film was preceded by the opening credits of the show. The [[Dremel]] website incident happened on [[October 31]], [[2004]] and featured a pumpkin carving kit for [[Halloween]] and linked to a [[Goatse.cx|Goatse]] pumpkin image as an example of what could be achieved. GNAA members then added their logo to the [[pumpkin]] image, leading visitors to think the GNAA had [[hack]]ed the [[Dremel]] website. {{ref|dremel}}

In October 2005, GNAA member Grog received "staff" status on the [[Freenode]] IRC network from [[Rob Levin]] (lilo) by posing as [[Greg Lehey]], famed developer of [[FreeBSD]] and [[MySQL]], who happened to have a similar irc nickname. Grog proceeded to un[[Jupe_(IRC)|jupe]] #GNAA, [[Jupe_(IRC)|jupe]] several of the more popular channels including: #wikipedia, #linux, and #solaris, and overall caused [[FUD]]. [[Rob Levin]] covered up his own mistake by claiming a staff member had been [[hacked]]. {{ref|freenode}}

===Pranking===
The GNAA runs a [[conference call]] system which they use to [[troll]] various companies and people such as [[America Online]]. They eventually produced an [[MP3]] file which combines excerpts from their various prank calls to America Online with the "Hey, everybody! I'm looking at [[homosexuality|gay]] [[pornography|porno]]!" sample from Last Measure.

===Counter-measures===
Because of the activities the GNAA performs online, various websites instituted methods in an effort to stop or curb the amount of [[Internet troll|trolling]] by the GNAA. Slashdot has a moderation system that is supposed to curb activities such as "First posting", and the website explains that first post comments are usually ''"one of those odd little [[meme]]tic hiccups that come out of nowhere and run amok."'' Their system moderates these posts and downgrades them for being off topic and makes them almost unreadable. This Slashdot tool is key, since the GNAA requires a user to perform a "first post" in order to join the GNAA. Slashdot and other websites also began to ban users for performing GNAA related acts or began to ban open-[[proxy]] addresses to prevent [[spamming]]. Users at different forums also have made fun of the GNAA and their members and have mocked their activities. In the words of one unimpressed Brawl-Hall poster: ''"Sorry, junior, but a Spam-a-thon that lasts fifteen minutes and taking over an IRC chat ain't a 'win'. Maybe you could take over some AOL chatrooms too, then you'd be 'teh c00l', right? Hah, what a joke."'' {{ref|BrawlHall}} It should be noted that Brawl-Hall was later made a complete mockery of at the hands of one or more GNAA members and has since closed almost completely. Slashdot has also called the GNAA, along with [[Trollkore]] and [http://anti-slash.org anti-slash.org], the "axis of abuse" in a parody of the [[axis of evil]].

The GNAA have been recognised as being deliberately disruptive by several organisations. For instance, on [[Freenode]]'s IRC server, the #GNAA channel redirects to ##you_have_got_to_be_kidding with a warning message indicating that the network might be inappropriate. This is standard Freenode behavior for [[jupe (IRC)|juped]] channels. Other IRC networks similarly jupe #GNAA. [[Jodi Dean]], Associate Professor of Political Science ([[Hobart and William Smith Colleges]]), in a presentation on blogging for a Cultural Studies Association meeting in Tuscon, noted that when she started blogging she was disturbed by [[neo-Nazi]] attacks and that:

:''"I've also been unsettled by those I can't place, those who may be satirical, performative in non-pc ways, and those whose comments are just generally disruptive and malicious. For example, one guy posted from the GNAA—which seems to be an anti-blog group with various satirical elements and strategies for irritating bloggers. GNAA stands for Gay Nigger Association of America and apparently gets its name from a short 1992 Danish movie called Gay Niggers from Outerspace, a film that appears to be an actual movie, a porn send up, but I can't be completely sure."'' {{ref|JodiDean}}

A growing number of highly motivated individuals who are against GNAA's neo-nazi message can be found on the internet. Counter-measures such as constant petitioning of GNAA members ISP's and website hosting companies for the removal of the neo-nazi, racist and homphobic material is thought to be a good basic first step.

Recently, [[Freenode]] began blocking people using open SOCKS [[proxies]] from connecting to their network, caused mainly by massive flooding of the Freenode network by GNAA member Rucas using his [[Perl]] [[Scripting programming language|script]], ASIAN.

==GNAA-UK==
GNAA also have a United Kingdom branch. 
Their website address is: www.gnauk.co.uk. 

==See also==
*[[Internet troll]]
*[[l0de Radio Hour]]
*[[Slashdot trolling phenomena]]
*[[Trolltalk]]

== References ==
# {{note|GNAAmotives}} [http://pepper.idge.net/gnaa/gnaa-aimgirl.txt Announcement of Aimgirl disruption]
# {{note|lode}} [http://www.instantlobotomy.com/ Announcement of l0de's death from his website]
# {{note|slashdot}} Slashdot – [http://slashdot.org/~michael/freaks Editor Michael's "freaks list"] – [http://apple.slashdot.org/article.pl?sid=05/06/12/130234&tid=179&tid=1 ''Mac OS X 10.4 Tiger for x86 Leaked?''] ([[June 12]] [[2005]])
# {{note|kuro5hin}} [http://www.kuro5hin.org/story/2004/12/28/161214/43 http://www.kuro5hin.org/story/2004/12/28/161214/43]
# {{note|somethingawful}} [http://forums.somethingawful.com/showthread.php?s=&threadid=724028 Something Awful thread] (Must be able to login to see the page)
# {{note|macrumors}} Mac Rumours - [http://www.macrumors.com/pages/2004/06/20040626041303.shtml Mac OS X 10.4 (Tiger) Screenshots?] ([[June 26]] [[2004]]) ([http://forums.macrumors.com/archive/index.php/t-77079 discussion]) – [http://www.macrumors.com/pages/2004/06/20040627202026.shtml WWDC, Photos and More on Tiger] ([[June 27]] [[2004]])
# {{note|appleinsider}} [http://www.appleinsider.com/article.php?id=520 http://www.appleinsider.com/article.php?id=520]
# {{note|dremel}} [http://216.234.51.66/board/showthread.php?s=&threadid=79383 forum discussing the Goatse GNAA image on the Dremel website] ([[October 31]] [[2004]])
# {{note|macdailynews}} [http://macdailynews.com/index.php/weblog/comments/6012/ "Report: Apple Mac OS X 10.4.1 for Intel hits piracy sites"], ''Mac Daily News'', [[June 11]] [[2005]]
# {{note|gnauk}} GNAUK – [http://media.gnauk.co.uk/aots-gnaa.mpg G4TV Attack of the Show footage] – [http://www.gnauk.co.uk/gnaa_osx2/ Fake OSX #2] – [http://www.gnauk.co.uk/gnaa_hp/ Harry Potter on Bittorrent] – [http://www.gnauk.co.uk/gnaa_hp2/ Harry Potter spoilers in forum]
# {{note|anti-slash}} [http://forums.anti-slash.org/viewtopic.php?t=577 http://forums.anti-slash.org/viewtopic.php?t=577]
# {{note|BrawlHall}} [http://brawl-hall.com/forums/printthread.php?t=58637 GNAA Thread]
#{{note|freenode}}[http://www.gnauk.co.uk/gnaa_freenode/index.php lilo gives GNAA staff status on Freenode] IRC logs before and after.
# {{note|JodiDean}} [http://jdeanicite.typepad.com/i_cite/2005/04/blogging_theory.html I cite : Blogging Theory], [[April 24]] [[2005]]. Jodi's presentation can be found [http://jdeanicite.typepad.com/i_cite/files/tuscon_talk.doc here].

== External links ==
*[http://www.gnaa.us GNAA Site] (watch out for links on the page, clicking on the members link opens shock pictures)
*[http://www.google.com/search?q=GNAA+site%3Aslashdot.org Google: Query for name GNAA on Slashdot website]
*{{imdb title|id=0274518|title=Gayniggers from Outer Space}}
*"James A. C. Joyce" (GNAA member rolloffle) ([[February 3]] [[2004]]). [http://www.kuro5hin.org/story/2004/2/2/171117/8823 Why your Movable Type blog must die]. ''Kuro5hin.org''.
*[http://www.gnauk.co.uk GNAUK] - this United Kingdom branch is mentioned in some GNAA press releases ('''sources''': [http://www.gnauk.co.uk/press/gnaa-europe 1], [http://www.gnauk.co.uk/press/gnaa-ptnntp 2], [http://www.gnauk.co.uk/press/gnaa-3kblog 3])
*[http://www.encyclopediadramatica.com/index.php/GNAA Article on the GNAA] at [[Encyclopædia Dramatica]]. (Warning: a photo of [[Goatse.cx|Goatse]] is used in the article)
*[http://lastmeasure.com Last Measure.com] (Warning: may contain [[shock images]])

[[Category:Slashdot]]
[[Category:Internet trolling]]

[[fr:Gay Nigger Association of America]]
[[simple:Gay Nigger Association of America]]

Unterschwelliger Reiz

2005-07-25T02:45:45Z

Simetrical: Changed disambig format, removed scare wording/claim, cut out a basically confusing and off-topic sentence to allow the first two paragraphs to be merged

:'''''Subliminal''' redirects here. For information on the Israeli rapper, see [[Subliminal (rapper)]]''

A '''subliminal message''' is a [[signal]] or [[message]] designed to pass below (sub) the normal limits of [[perception]]. For example it might be inaudible to the [[conscious]] mind (but audible to the [[unconscious]] or deeper [[mind]]) or might be an image transmitted briefly and unperceived consciously and yet perceived unconsciously. In the everyday world, many have claimed that subliminal techniques are used in [[advertising]] and for [[propaganda]] purposes, but no such claim has ever been verified.

==Origin of the Term==

The term ''subliminal message'' was popularized in a [[1957]] book entitled ''[[The Hidden Persuaders]]'' by [[Vance Packard]]. This book detailed a study of movie theaters that supposedly used subliminal commands to increase the sales of [[popcorn]] and [[Coca-Cola]] at their concession stands. However, [[James Vicary]] (the author of the study) later admitted the study was fabricated.

In [[1973]] [[Wilson Bryan Key]]'s book ''[[Subliminal Seduction]]'' claimed that subliminal techniques were in wide use in advertising. The book contributed to a general climate of fear with regard to [[Orwellian]] dangers (of subliminal messaging). Public concern was enough to lead the [[Federal Communications Commission]] to hold hearings and to declare subliminal advertising "contrary to the public interest" because it involved "intentional deception" of the public.

==Validity==

In spite of the popular belief that subliminal messages are widely used to influence audiences, there is little evidence that the technique has ever been used on a mass audience (other than its occasional use by artists who use it to make an artistic statement). While there is some evidence that subliminal messages can affect the observer, the current consensus among marketing professionals is that subliminal advertising is ineffective and can be counter-productive. The theory underlying subliminal messages is often considered to be [[pseudoscience]]. However, the concept of subliminal messages is very popular among [[conspiracy theory|conspiracy theorists]], and most people in media-saturated areas (such as the [[United States]]) are familiar with the term.

A number of fringe elements in society have made occasional claims that subliminal messages can be found in various forms of popular entertainment. Popular claims of subliminal commands include the supposed use of "[[backward message]]s" in [[rock and roll]] songs. Conservative activist [[Donald Wildmon]] has claimed that [[The Walt Disney Company]] inserted the subliminal command "SEX" into the [[animation|animated]] film ''[[The Lion King]]'' (see that article for more information on this). Mainstream authorities have generally ignored these claims due to the dubious reputations of their authors.

The most credible form of subliminal messages involves the use of graphics with components that can be interpreted ambiguously. Surrealistic artists have explored these methods by distorting objects to create associations of unrelated themes. Joe Camel, a cartoon character used to advertise Camel cigarettes, had a smirk with a cigarette hanging from the lips when viewed in its totality. However, its snout looked like a scrotum, and the flare of the nose could also be interpreted as the labia of a vagina being penetrated by a penis (the nose of the camel). Joe Camel was an advertising tool that subliminally tantalized with sex to overcome the aversion to a harmful product. Cartoons were banned from cigarette advertisements in the late 1990s because they were seen as targeting young people.

==Discussion==

Subliminal perception or cognition, can be considered a subset of unconscious [[cognition]] where the forms of unconscious cognition also include attending to one signal in a noisy environment while unconsciously keeping track of other signals (e.g. one voice out of many in a crowded room) and tasks done automatically.

An important question about subliminal perception is: How much of the unattended or unconscious signal or message is perceived? That is, is the whole message sensed and fully digested or perhaps only its main and simpler features? There are at least two schools of thought about this. One of them argues that only the simpler features of unconscious signals could be perceived. The second school of thought argues that unconscious cognition is comprehensive and that much more is perceived than can be verbalized.

Various types of studies of subliminal perception have been conducted. The findings of recent studies demonstrate that subliminal stimuli can influence behavior and subsequent perceptions but it is as yet unclear how these results may generalize to real world settings. A related field is the question of whether [[Anesthesia|anaesthetized]] patients are completely unaware whilst apparently completely asleep/unconscious.

Proponents of the power of subliminal messages claim they gain influence or power from the fact that they circumvent the critical functions of the conscious mind, and therefore subliminal suggestions are potentially more powerful than ordinary suggestions. This route to influence or persuasion would be akin to [[auto-suggestion]] or [[hypnosis]] wherein the subject is encouraged to be (or somehow induced to be) relaxed so that suggestions are directed to deeper (more gullible) parts of the mind; some observers have argued that the unconscious mind is incapable of critical refusal of hypnotic or subliminal suggestions.

However, research findings do not support the conclusion that subliminal suggestions are peculiarly powerful, or even have any effect at all.

===Subliminal Messages in Advertising===

A form of subliminal messaging commonly believed to exist involves the insertion of "hidden" messages into [[film|movie]]s and [[Television|TV]] programs. The concept of "moving pictures" relies on [[persistence of vision]] to create the illusion of movement in a series of images projected at 23 to 50 frames per second; the popular theory of subliminal messages usually suggests that subliminal commands can be inserted into this sequence at the rate of perhaps 1 frame in 25 (or roughly 1 frame per second, with a duration of about 1/25 of 1 second). The hidden command in a single frame will flash across the screen so quickly that it is not consciously perceived, but the command will supposedly appeal to the subconscious mind of the viewer, and thus have some measurable effect in terms of behavior.

Another "subliminal" message technique is supposedly to embed into a printed advertisement certain messages or symbols which are subtle and perceived only by the unconscious mind, either to communicate a message or to increase the attention paid to the printed ad. This technique, as with subliminal TV advertising, is not generally regarded as effective.

As to the question of whether subliminal messages are widely used to influence groups of people e.g. audiences, there is no evidence to suggest that any serious or sustained attempt has been made to use the technology on a mass audience. The widespread reports that arose in [[1957]] to the effect that customers in a movie theatre in New Jersey had been induced by subliminal messages to consume more popcorn and more [[Coca-Cola]] were almost certainly false. The current consensus among marketing professionals is that subliminal advertising is counter-productive. To some this is because they believe it to be ineffective, but to most it is because they realise it would be a public relations disaster if its use were discovered. Many have misgivings about using it in marketing campaigns due to ethical considerations.

During the [[2000 U.S. presidential campaign]], a [[television]] ad [[campaign]]ing for [[United States Republican Party|Republican]] candidate [[George W. Bush]] showed words (and parts thereof) scaling from the foreground to the background on a television screen. When the word <tt>BUREAUCRATS</tt> flashed on the screen, one frame showed only the last part, <tt>RATS</tt>. [[United States Democratic Party|Democrats]] promptly asked the [[Federal Communications Commission|FCC]] to look into the matter, but no penalties were ever assessed in the case. The effect this had on the overall presidential race was unclear; the [[United States Democratic Party|Democrats]] and [[Al Gore]] received ridicule for finding malicious intent in something that could have been a simple mistake; the [[United States Republican Party|Republicans]] received ridicule for the lack of attention to detail and Bush's mispronunciation of "subliminal" (it came out as "subliminable").

== See also ==

*[[advertising]]
*[[marketing]]
*[[promotion]]
*[[backmasking]]
*[[list of notorious subliminal messages]]

== Quotations ==
* "Over the years there have been literally hundreds of studies"..."these studies show that considerable information capable of informing decisions and guiding actions is perceived even when observers do not experience any awareness of perceiving". Philip Merikle, Department of Psychology, [[University of Waterloo]].

==External links==
*[http://www.snopes2.com/business/hidden/popcorn.htm Urban Legends: Subliminal Advertising]
*[http://www.scientificpsychic.com/graphics/index.html Optical Illusions and Visual Paradoxes]
*[http://www.stayfreemagazine.org/archives/22/subliminal-advertising.html Subliminal Seduction: How Did the Uproar over Subliminal Advertising Affect the Advertising Industry?]
*[http://www.parascope.com/articles/0497/sublimdc.htm 1984 testimony about subliminal messages to the Federal Communications commission]
*[http://www.nlpschedule.com/random/sublm00.html Subliminal Influence and NLP Article]
*[http://www.csicop.org/si/9611/judas_priest.html/ Scientific Consensus and Expert Testimony: Lessons from the Judas Priest Trial]
*[http://www3.telus.net/jefmil/stairwaybackwards.htm Subliminal messages in music]

==References==
* Subliminal Perception: The nature of a controversy, N.F.Dixon, McGraw-Hill, New York, 1971.
* Psychological Investigations of Unconscious Perception, [[Journal of Consciousness Studies]], P.M Merikle and M. Daneman, 1998.
* New Look 3: Unconscious Cognition Reclaimed, American Psychologist, 47, Anthony W. Greenwald, 1992.
* Holender, D. (1986). Semantic activation without conscious identification in dichotic listening, parafoveal vision, and visual masking: A survey and appraisal. Behavioral and Brain Sciences, 9, 1-23.
* Seitz and Watanabe. (2003). Is subliminal learning really passive. Nautre,422, 36.
[[es:Mensaje subliminal]]
[[he:מסר תת סיפי]]
[[fi:Subliminaalinen]]
[[ro:Mesaje_subliminale]]
[[sv:Subliminal perception]]

[[Category:Perception]]
[[Category:Popular psychology]]
[[Category:Advertising]]
[[category:Promotion and marketing communications]]
[[Category:Marketing]]

Konversion (Judentum)

2005-06-23T04:59:10Z

Simetrical: /* History */ "Proselyte" is English, "προσήλυτος" is Greek

:''See also: [[Religious conversion#Conversion to Judaism|Conversion to Judaism]]''.

'''Ger tzedek''' ([[Hebrew language|Hebrew]]: "righteous convert" or "convert [of] righteousness") or '''Ger''' ("stranger" or "convert") or is a [[gentile]] (i.e. a non-[[Jew]] by birth) who has undergone ''giur'' ([[Religious conversion#Conversion to Judaism|religious conversion]]) to [[Judaism]] by fulfilling the ritual requirements for such conversion accepting the obligations of Jewish religious observance.

==History==

In [[Tanakh|Biblical]] [[Hebrew language|Hebrew]], the word ''ger'' can denote either a convert (and is usually interpreted as such by the [[Talmud]]) or a non-Jewish inhabitant of the [[Land of Israel]] who observes the seven [[Noahide Laws]] and has repudiated all links with idolatry. The word ''ger tzedek'' was used to denote a full convert. In post-Talmudic times, the word ''ger'' has become synonymous with ''ger tzedek''; ''Ger'' is commonly translated by the word "proselyte", and has come to mean a convert to Judaism.

===Motivations for conversion===

A mystical interpretation of conversions to [[Judaism]] is that there a convert is someone with a [[Jew]]ish ''neshama'' (soul) who is simply trying to find his/her way home.

In general terms, anyone who commits to living a religiously observant life is an acceptable candidate for conversion. For a variety of reasons, [[rabbi]]s have traditionally discouraged people from converting to Judaism, and most will insist that the candidate for conversion demonstrate his/her commitment in word and deed before the conversion is undertaken.

A number of reasons for converting exist: some have theological convictions consistent with Judaism; others are attracted to elements of Jewish religious life; some wish to belong to a particular Jewish community. A significant portion wish to convert because they want to marry someone who is Jewish. This latter reason (see [[secondary conversion]]) is considered to be insufficient by most [[Orthodox Judaism|Orthodox]] rabbis.

===Traditional requirements===
The requirements under ''[[halakha]]'' for [[religious conversion|conversion]] to [[Judaism]] are that a ''[[beth din]]'' witnesses and approves:
*[[Circumcision]] (''[[Brit milah]]'') for men
*Immersion (''t'vilah'') in a ''[[mikveh]]'' (ritual bath)
*Understanding and acceptance of the obligations of being a religiously observant [[Jew]].

After confirming that all these criteria have been met, the ''beth din'' issues a ''Shtar Giur'' ("Certificate of Conversion"), certifying that the former [[gentile]] is now a Jew.

===Variations and controversy===

The requirements for conversion to Judaism are intended to avoid any uncertainty about a convert's true status. The certification by a ''[[beth din]]'' was based on events the completeness of which were carefully defined.

The [[Reform Judaism|Reform]] movement has relaxed some of the requirements for conversion, notably by making ''[[brit milah]]'' optional, only encouraging ''t'vilah'' (immersion), and requiring that converts commit to religious standards set by the Reform movement.

Both the [[Conservative Judaism|Conservative]] and [[Orthodox Judaism|Orthodox]] movements require that all ''[[halakha|halakhic]]'' requirements be met, but they differ on what constitutes a competent ''beth din''. Orthodox rabbis generally do not accept the authority of non-Orthodox rabbis. Moreover, in Orthodoxy, a person who converts under the guidance of a non-Orthodox rabbi is presumed to have an incomplete or erroneous understanding of the law he or she is taking upon him or herself; therefore, Orthodox rabbis generally do not accept conversions under Conservative (or Reform, or [[Reconstructionist Judaism|Reconstructionist]]) auspices.

Since the Orthodox movement is not organized in a unified way, Orthodox rabbis will not automatically accept each other's authority. This has led to a general reluctance in the Orthodox communities to prepare and perform conversions.

===Consequences of conversion===
Once undergone, a religious conversion to Judaism is irreversible, unless there are grounds to believe that the convert was insincere during the conversion process. In such cases - which are rare - a ''[[beth din]]'' may annul the conversion.

===Place in religious life===
Halakha forbids reminding a convert that he/she was once not a [[Jew]] and hence little distinction is made in Judaism between "Jews by birth" and "Jews by choice." According to halakha, converts face a limited number of restrictions, e.g. they cannot marry Kohanim. Converts can become rabbis (and some have).

==See also==
*[[Abraham ben Abraham]]
*[[List of converts to Judaism]]
*[[Religious conversion]]
*[[Ger toshav]]

==External links==
*[http://www.convert.org/ Conversion to Judaism homepage] - information on conversion within all branches of Judaism in North America
*[http://www.itim.org.il/bin/en.jsp?enDispWho=CeremonySuperTopic%5El6&enPage=BlankPage_E&enDisplay=view&enDispWhat=object&enZone=CeremonySuperTopic&enInfolet=viewObject_E.jsp Conversion to Judaism] on the Itim site (practical information on Orthodox conversion through the Israeli Chief Rabbinate and conversion in the diaspora).
*[http://shamash.org/lists/scj-faq/HTML/rl/int-intro.html Intermarriage and Conversion Reading List Introduction]
*Frequently asked questions:
**[http://www.shamash.org/lists/scj-faq/HTML/faq/10-07.html How does one convert?]
**[http://www.shamash.org/lists/scj-faq/HTML/faq/10-13.html Why is the conversion process so complicated?]
**[http://www.shamash.org/lists/scj-faq/HTML/faq/10-08.html What about adults who are not circumcised?]
**[http://www.shamash.org/lists/scj-faq/HTML/faq/10-14.html What is the status of a child when the mother converts to Judaism during pregnancy?]

[[Category:Jews]]
[[Category:Jewish law and rituals]]
[[Category:Hebrew words]]

[[he:גיור]]

Englisches Alphabet

2005-06-15T05:52:45Z

Simetrical: /* Notes */ Strengthened example, added sentence

The '''[[English language]]''' has been written using the '''[[Latin alphabet]]''' from ca. the [[7th century]]. Since the [[5th century]], the [[Anglo-Saxon Futhorc]] had been used, and both alphabets continued to be used in parallel for some time. Use of the Latin alphabet was influenced by the Futhorc: the letters [[þ]] (thorn) and {{Unicode|[[Wynn|ƿ]]}} (wynn) are derived from [[runes]]. The letter [[ð]] (eth) was devised as a modified version of [[d]], and {{Unicode|[[Yogh|ȝ]]}} (yogh) was created by Norman scribes who derived it from the form of the [[insular script|insular]] [[g]] used in Old English and [[Irish language|Irish]] alongside their own [[Carolingian minuscule|Carolingian]] '''g'''. This resulted in an English alphabet which consisted of a total of 27 letters (the 23 letters of the post-[[1st century BC]] Latin alphabet, one modified Latin letter, two letters borrowed from Runic, and one letter borrowed from the Insular Latin hand). Additionally, the [[ligature]]s [[w]] (for '''vv''') and [[æ]] (named "ash", for ''ae'') were in use.

In [[Modern English]] [[orthography]], '''þ''', '''{{Unicode|ȝ}}''', '''ð''', and '''{{Unicode|ƿ}}''' are obsolete, although '''þ''' continued its existence for some time, its lower case form gradually becoming graphically indistinguishable from the minuscule [[y]] in most handwritings. On the other hand, [[u]] and [[j]] were introduced as distinct from [[v]] and [[i]] in the [[16th century]], and '''w''' assumed the status of an independent letter, so that the English alphabet is now considered to consist of the following 26 letters:

{|
| Letter    || Letter name ([[International Phonetic Alphabet|IPA]])
|-
| [[A]] || a {{IPA|[eɪ]}}
|-
| [[B]] || bee {{IPA|[biː]}}
|-
| [[C]] || cee {{IPA|[siː]}}
|-
| [[D]] || dee {{IPA|[diː]}}
|-
| [[E]] || e {{IPA|[iː]}}
|-
| [[F]] || ef {{IPA|[ɛf]}}
|-
| [[G]] || gee {{IPA|[dʒiː]}}
|-
| [[H]] || aitch {{IPA|[eɪtʃ]}} or haitch {{IPA|[heɪtʃ]}}
|-
| [[I]] || i {{IPA|[aɪ]}}
|-
| [[J]] || jay {{IPA|[dʒeɪ]}}
|-
| [[K]] || kay {{IPA|[keɪ]}}
|-
| [[L]] || el {{IPA|[ɛl]}}
|-
| [[M]] || em {{IPA|[ɛm]}}
|-
| [[N]] || en {{IPA|[ɛn]}}
|-
| [[O]] || o {{IPA|[oʊ]}} ([[American English]]) or {{IPA|[əʊ]}} ([[Received Pronunciation]])
|-
| [[P]] || pee {{IPA|[piː]}}
|-
| [[Q]] || cue {{IPA|[kjuː]}}
|-
| [[R]] || ar {{IPA|[ɑː]}} ([[rhotic and non-rhotic accents|non-rhotic]]) or {{IPA|[ɑɹ]}} (rhotic)
|-
| [[S]] || ess {{IPA|[ɛs]}}
|-
| [[T]] || tee {{IPA|[tiː]}}
|-
| [[U]] || u {{IPA|[juː]}}
|-
| [[V]] || vee {{IPA|[viː]}}
|-
| [[W]] || double-u {{IPA|[dʌb(ə)l juː]}}
|-
| [[X]] || ex {{IPA|[ɛks]}}
|-
| [[Y]] || wye {{IPA|[waɪ]}}
|-
| [[Z]] || zed {{IPA|[zɛd]}} or zee {{IPA|[ziː]}} (the latter in [[American English]] only)
|}

Unfortunately, these common names for the letters are often hard to distinguish from each other when heard.
The [[NATO phonetic alphabet]] gives each letter a name specifically designed to sound different from any other.
Therefore, [[aircraft]] pilots and many other people use the NATO phonetic alphabet names instead of these common names.

== Notes ==

The letters A, E, I, O, U are [[vowel]]s; sometimes Y and rarely W function as vowels too, but more often they're [[semivowel]]s. The remaining letters are [[consonant]]s. The letter most frequently used in [[English language|English]] is E. The least frequent used letters are Q, X, and Z.

The names of the letters are rarely spelled out, except in compound words like ''tee-shirt'', ''deejay'', ''u-turn'', ''emcee'', ''okay'', etc., and derived forms like ''exed out'', ''effing''. The forms listed here are from the [[Oxford English Dictionary]]: vowels stand for themselves, and consonants are ''C+ee'' or ''e+C'', with the exceptions of ''aitch, jay, kay, cue, ar, ess, wye, zed''.

[[Diacritic]] marks are not common in English, appearing mainly in foreign and loan-words such as ''résumé'' and ''façade''. Occasionally, especially in older writing, diacritics are used to indicate the [[syllable]]s of a word: ''cursed'' is pronounced with only one syllable, while ''cursèd'' would be pronounced with two; similarly ''coop'' (one syllable, a structure most strongly associated with chickens) versus ''coöp'' or more commonly ''co-op'' (two syllables, informal contraction of ''[[cooperative]]''). These distinctions are, however, optional, and often unused even where they would serve to alleviate some degree of confusion. See also [[English language#Written accents|Written accents in English]].

The English alphabet is a form of the [[Latin alphabet]]. The lower-case letters, W, and the distinctions between I and J, U and V were introduced in continental [[Europe]] during the [[Middle Ages]]. The Roman ligatures [[Æ]] and [[OE ligature|Œ]] are still used in [[British English]] for certain words of Greek or Latin origin, such as "[[encyclopedia|encyclopædia]]" and "[[body cavity|cœlom]]".

In [[Old English language|Old English]], Æ was adopted as a letter on its own and called ''æsc'' ("ash"), and in very early Old English Œ also appeared as a distinct letter named ''œðel''. Other Old English letters (also used in [[Middle English]] and modern [[Icelandic language|Icelandic]]) are [[Þ]] (''thorn'') and [[Ð]] (''eth''), both now ''th'' with the exception of being ''y'' in a few archaisms like ''Ye Olde Booke Shoppe''. (When the letter wye was adopted during Middle English, it had a dot over it to distinguish it from thorn, so in such archaisms ''y'' without a dot is thorn, not wye.) Other archaic letters are runic {{Unicode|Ƿ}} (''[[wynn]]''), now uniformly replaced by W; and a variant form of G, {{Unicode|Ȝ}} (''[[yogh]]''), which was later replaced by Y (''young''), W (''bow''), or GH (''night, laugh''). The variant lower-case form {{Unicode|ſ}} (''[[long s]]'') lasted into [[Early Modern English|early modern English]], and was used in non-final position up to the early nineteenth century.

Historically the [[ampersand]] (&) was treated as the twenty-seventh letter of the English alphabet, although the figure is properly a [[ligature]] for the letters ''et''. It is used to represent the English word ''and'' and occasionally the Latin word ''et'', as in the abbreviation ''&c'' (et cetera).

== See also ==
* [[Alphabet]]
* [[Latin alphabet]]
* [[ASCII]]
* [[Anglo-Saxon Futhorc]]
* [[English language]]
* [[History of the English language]]
* [[Alphabets derived from the Latin]]

[[Category:English spelling|Alphabet]]
[[Category:Latin-derived alphabets|English]]
[[cs:Anglick%C3%A1 abeceda]]

Pseudosphäre

2005-03-20T21:53:13Z

Simetrical:

In [[geometry]], a '''pseudosphere''' or '''tractricoid''' is the result of revolving a [[tractrix]] about its [[asymptote]]. It has constant negative Gauss [[curvature]], except at the [[cusp]], and therefore is locally isometric to a [[hyperbolic plane]] (everywhere except for the cusp).

{{geometry-stub}}
[[Category:Differential geometry]]
[[Category:Surfaces]]

Creative Assembly

2005-03-04T22:14:56Z

Simetrical:

The Creative Assembly is the developer of such [[strategy]] games such as [[Medieval: Total War]] and [[Rome: Total War]]. They are based in the UK.
{{cvg-stub}}

Ralph Alger Bagnold

2005-01-03T21:52:39Z

Simetrical: /* Desert Innovation */ Made "sun compass" one link

'''Ralph A. Bagnold''' ([[April 3]] [[1896]] - [[May 28]] [[1990]]), during [[World War II]], was the founder and first commander of the [[British Army]]'s [[Long Range Desert Group]]. He is also generally considered to have been a "[[pioneer]]" of [[desert]] exploration, an acclaim earned for his activities during the [[1930s]]. These included the first recorded east-west crossing of the [[Libyan Desert]] ([[1932]]). Bagnold was also a veteran of [[World War I]]. He held a degree in [[engineering]] and was the author of ''[[The Physics of Blown Sand]]'' (''[[1941]]''), which has been used by [[NASA]] in studying [[sand]] [[dune]]s on [[Mars (planet)|Mars]].

==Desert Innovation==

He is credited with developing a [[sun compass]], which is not affected by [[metal]] [[vehicle]]s as a [[magnetism|magnetic]] compass might be. During the 1930s his group also began the practice of reducing [[tire]] [[pressure]] when [[driving]] over loose sand.

In addition, Bagnold is credited with discovering a method of driving over the large sand dunes found in the "sand [[sea]]s" of the Libyan Desert. He wrote, "I increased speed... A huge glaring wall of yellow shot up high into the sky. The [[truck|lorry]] tipped violently backwards - and we rose as in a lift, smoothly without vibration. We floated up on a yellow cloud. All the accustomed [[automobile|car]] movements had ceased; only the [[speedometer]] told us we were still moving fast. It was incredible..." However, noted [[Fitzroy Maclean]], "too much dash had its penalties. Many of the dunes fell away sharply at the far side and if you arrived at the top at full speed, you were likely to plunge headlong over the precipice...and end up with your [[truck]] upside down on top of you."

==World War II==
Bagnold wrote, "Never in our peacetime travels had we imagined that war could ever reach the enormous empty solitudes of the inner desert, walled of by sheer distance, lack of water, and impassable seas of sand dunes. Little did we dream that any of the special equipment and techniques we had evolved for very long-distance travel, and for navigation, would ever be put to serious use."

After [[Italy]] declared war on Britain, Bagnold requested an interview with [[Archibald Wavell|General Wavell]] and asked permission to create a mobile scouting force. Wavell asked him what he would do if he found the Italians were not doing anything in the desert, Bagnold then suggested that his unit might be able to commit acts of "piracy". Bagnold was given six weeks to form his unit under the conditions that any request he might make of "should be met instantly and without question." This unit would become the [[Long Range Desert Group]].

See also:

* [[Pat Clayton|Clayton, Pat]]
* [[Bill Shaw|Shaw, Bill]]

[[Category:1896 births|Bagnold, Ralph A.]]
[[Category:1990 deaths|Bagnold, Ralph A.]]
[[Category:British Army officers|Bagnold, Ralph A.]]