User:IntegralPython/sandbox

My sandbox, for drafting articles or saving them because I feel like it.

Stuff

What is Algebra

What is algebra? Algebra is a multifaceted branch of mathematics with many parts that are vastly different from others. Essentially, algebra is manipulation of symbols based on given properties about them. For instance, elementary algebra is about manipulating variables, which are abstractions of numbers in a number system. The variables in the number system are only allowed to have properties that are shared by every number it represents, and vice versa. The most simple parts of algebra begin with computations similar to those of arithmetic but with variables standing for numbers. This allowed proofs of properties that are true no matter which numbers are involved. For example, in the quadratic equation $ax^{2}+bx+c=0,$ $a,b,c$ can be any numbers whatsoever (except that $a$ cannot be $0$), and the quadratic formula can be used to quickly and easily find the values of the unknown quantity $x$ which satisfy the equation, known as finding the solutions of the equation. Historically, the study of algebra starts with the solving of equations such as the quadratic equation above. The study of these equations lead to more general questions that are considered, such as "does an equation have a solution?", "how many solutions does an equation have?", and "what can be said about the nature of the solutions?". These questions lead to ideas of form, structure and symmetry. Because algebra is simply the manipulation of entities, there is no rule that states that only numbers and variables that stand for numbers are allowed. In this way, algebra is extended to consider entities that do not stand for just one number, such as vectors, matrices, and polynomials. Many of these and the previously mentioned manipulation of variables form the basis of high school algebra, while others form subjects such as linear algebra. Even though algebra had already expanded into manipulations of many numbers in the defined topics above, it is possible to define entities that are unlike any familiar numbers. These entities are created using only their properties, and involve strict definitions that create a set of entities that work together with their properties. The entities form algebraic structures such as groups, rings, and fields. Abstract algebra is the study of these entities and more. In short, the study of algebra involves any set of items which share properties. As long as it is possible to distill the similarities into similar sets that relate to one another in different ways, it is a part of algebra. Today, algebra has grown until it includes many branches of mathematics, as can be seen in the Mathematics Subject Classification where none of the first level areas (two digit entries) is called algebra. Today algebra includes section 08-General algebraic systems, 12-Field theory and polynomials, 13-Commutative algebra, 15-Linear and multilinear algebra; matrix theory, 16-Associative rings and algebras, 17-Nonassociative rings and algebras, 18-Category theory; homological algebra, 19-K-theory and 20-Group theory. Algebra is also used extensively in 11-Number theory and 14-Algebraic geometry.

Antiassociative algebra
Antiassociative algebra An algebra antiassociative if (xy)z = -x(yz) for every case of x,y, and z.

Ugandan knuckles

Ugandan Knuckles Ugandan Knuckles is an internet meme from January 2018 depicting a deformed version of Knuckles the Echidna. Players would go in hords to the virtual reality video game VRChat to troll other players. The people would say quotes such as "Do you know the way?", which originate from the 2010 Ugandan action film Who Killed Captain Alex?, as well as "spitting" on other users whom they felt did not know "de way". The meme was a significant trend followed by several news organisations, including USA Today. History On February 20 2017, YouTuber Gregzilla uploaded a video on Sonic Lost World featuring a parody picture of Knuckles the Echidna. On December 22 2017, a 3D model of the Knuckles sketch was released on DeviantArt. That day, YouTuber Stahlsby uploaded a video in which several VRChat players wearing the parody costume trolled others by making clicking noises and saying "You do not know the way". After that, more and more people flooded VRChat to troll others as Ugandan Knuckles, leading to controversy, as the mock Ugandan accent and quotations used were widely regarded as racist. However, The meme continued to gain popularity until about mid-January 2018, but had mostly subsided by February. Controversy Because of its use of a fake Ugandan accent as well as the quotations from Who Killed Captain Alex?, the meme was widely criticized for being racially insensitive; Polygon described it as problematic. On January 27 2018, the company Razer was brought under fire for posting a Ugandan Knuckles meme that was widely criticised as a racist misstep. The original creator of the 3D avatar, DeviantArt user "tidiestflyer", showed regret over the character, saying that he hoped it would not be used to annoy players of VRChat and that he enjoys the game and does not want to see anyone's rights get taken away because of the avatar. In response to the trolling in the game, the developers of VRChat published an open letter on Medium, stating that they were developing "new systems to allow the community to better self moderate" and asking users to use the built-in muting features.