Talk:Number

Grammar correction

Before reference 4, you have “ (and its combinations with real numbers by adding or subtracting its multiples).” It should be “(and it's combinations with real number by adding or subtracting it's multiples).” PP3CATWSPofficial (talk) 09:24, 30 May 2024 (UTC)

No: this text correctly uses the pronoun "its" (meaning "of it"), which does not contain an apostrophe. It's would be an abbreviation for "it is combinations" or possibly "it has combinations", which are not the intended meaning here. Certes (talk) 09:45, 30 May 2024 (UTC)

Oh yeah, you are right. I confused it with another rule, sorry! PP3CATWSPofficial (talk) 10:03, 31 May 2024 (UTC)

The distinctions among counting, measuring, and labelling

"A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words."

That's just real nice! However, the terms count, measure and label, all mean the same thing wrt number.

To count means to measure (notice?) in terms of the abstract unit. Once the counting or measuring is done, then we give the measure a name (same as "label", eh?).

Please take some time to revise this garbage article. It will benefit humanity in a way you cannot imagine!

https://www.academia.edu/125757733/Realisation_and_Development_of_Number_in_1_Page

Also, teach the four basic operations of arithmetic using ratios of magnitudes before a child learns about numbers:

https://www.academia.edu/124828666/Gabriel_arithmetic_without_numbers_a_method_based_on_Thales_proportionality_theorem

2A02:587:AF2D:8700:65F7:8F4D:5ED5:BA5E (talk) 08:09, 11 December 2024 (UTC)

In the perhaps unlikely event that you ever come back and read this, here are some comments on the nature of the three processes you referred to.

• I have a piece of string, and I wish to know how long it is. I put it against a ruler marked in millimetres, and find it is 127mm long; that is to say that it is 127 times as long as an arbitrarily chosen standard length called a "millimetre". I could have measured it instead against some other, equally arbitrary, standard length, and concluded that it was 5 inches long, or 12.7 centimetres, or 0.1389 yards, etc etc. Or I could have measured it in millimetres, but with a measuring instrument with a higher precision than my ruler, and concluded that it it 127.312mm long. That is what measuring is.
• I have some more pieces of string, and wish to know how many, so I check them, and find there are seven of them. I don't have to specify a unit, such as a millimetre, or a gram, or an hour, because there are just seven of them, and that is absolute, it is not a comparison with some arbitrary unit. I also don't need to consider a using a greater degree of precision, because there are just seven pieces: I know there can't be 7.183 pieces. That is what counting is.
• When I was a child, there were two slightly different versions of the bus route which came near to our house, which were called the 29 bus and the 29a bus. Then the people who ran the bus service decided they preferred to use just numbers, without letters. It made sense to have adjacent numbers for routes which were almost the same, and the numbers 28 & 30 were already allocated to other routes, so 29 & 29a were replaced by 90 & 91. There was no change in any measurement: neither the buses nor the bus routes became bigger. There was no change in any count: there were not suddenly more buses than there had been. What changed was the way that the buses were labelled.
• As for the way you chose to express yourself in suggesting to other people that it might be a good idea to consider making changes to the article, you may like to consider whether there might have been a better way of putting it. However, I expect you won't, will you? JBW (talk) 11:51, 11 December 2024 (UTC)

Last paragraph of lead

In modern mathematics, number systems are considered important special examples of more general algebraic structures such as rings and fields, and the application of the term "number" is a matter of convention, without fundamental significance.

I think I understand what this sentence is trying to get at, but IMO it needs to be made clearer for non-technical readers. To me this seems far too broad a claim. "Number" may be without "fundamental significance" in some specialised areas of mathematics, but it's not the case in general. TheGrifter80 (talk) 12:57, 14 September 2025 (UTC)

I rewrote the paragraph, hoping that this resolves the issue. D.Lazard (talk) 14:15, 14 September 2025 (UTC)

Yes I think that is an improvement, although a couple of further comments.

It might be better to have this follow in from the description of extensions of the number system.

The section in the lead on numerology/cultural aspects of numbers is a bit out of place as there is no real discussion of this in the article.

I am happy to have a go at making some of these changes. TheGrifter80 (talk) 07:01, 15 September 2025 (UTC)

How is this helpful?

The article includes the following statement which was apparently taken from an old encyclopedia entry:

Other noteworthy contributions have been made by Druckenmüller (1837), Kunze (1857), Lemke (1870), and Günther (1872).

It has since been oft repeated, but without clarification. I was able to track down Druckenmüller and Günther, but not the other two. There's no clue about what papers these are referencing. Any ideas? Praemonitus (talk) 05:15, 22 October 2025 (UTC)

The whole paragraph must be removed.

It consists only of a list of authors with references to their original work, without any indication of the results contained in these papers and without any source attesting that this list is relevant. This is a clear wp:original synthesis.

Except this list of authors, the only mathematical content of the paragraph is "Simple continued fractions, closely related to irrational numbers, ...". This "close relation" is neither explained nor sourced. It is also controversial, since simple continued fractions are only one tool, among many, for studying irrational numbers. So, the first sentence is also WP:OR.

By the way, the whole section must be completely rewritten. In particular, it contains "It was not, however, until the 19th century that mathematicians separated irrationals into algebraic and transcendental parts, and once more undertook the scientific study of irrationals. It had remained almost dormant since Euclid". This is completely wrong, since, looking to Simple continued fraction § History, it appears that many fundamental results on irrational numbers date from the 18th century. For example: the characterization of the irrational numbers as those that have an infinite continued fracion (Euler), the irrationality of e (Euler) and π (Lambert), the characterization of quadratic irrationals as periodic continued fractions (Lagrange). None of these results are mentioned here. D.Lazard (talk) 09:58, 22 October 2025 (UTC)

The suggestion of rewriting the whole section is probably a good one. I don't think I have enough knowledge of the subject to undertake that task, but there are a couple of changes that I do intend to make.

Not only does the paragraph containing the sentence quoted by Praemonitus consist largely of just a list of names without clear indication of what their relevant work was, but also the very small mentions of mathematical topics are about continued fractions and determinants, not numbers. Yes, of course there's a connection between continued fractions and numbers, but just stating that there is, with no indication if what the connection is, doesn't justify this content. I can see even less relevance of the mention of determinants. Adding to those thoughts the opinions expressed above by Praemonitus and D.Lazard, I intend to implement D.Lazard's suggestion of removing the paragraph.

The last sentence of the previous paragraph, about Galois's work, is not about numbers at all. Of course Galois theory has a connection to the subject of types of algebraic numbers, but there is no mention here of that connection. I therefore intend to remove that sentence. I'm also unsure about the rest of that paragraph. Was the Abel–Ruffini theorem responsible for the introduction of the concept of algebraic numbers? If it was, then all well and good, but if not then I don't see any justification for the statement about it in its present form. JBW (talk) 11:17, 22 October 2025 (UTC)

Thanks. I suspect the statement comes from this source (one paragraph up from the Bibliography):

Gilman, Daniel Coit; et al., eds. (1906). "Number". The New International Encyclopaedia. Vol. 14. Dodd, Mead. p. 676.

Praemonitus (talk) 14:33, 22 October 2025 (UTC)

I have renamed and largely edited the section § Real numbers and irrational numbers. The result is not very good, but certainly better and clearer than the previous version. D.Lazard (talk) 14:54, 22 October 2025 (UTC)

This whole section was largely copied, without attribution, from David Eugene Smith's 1896 History of Modern Mathematics. –jacobolus (t) 15:03, 22 October 2025 (UTC)