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The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers. This glossary is alphabetically sorted.
Domain-specific terms must be recategorized into the corresponding mathematical domain. If the domain is unclear, but reasonably believed to exist, it is better to put the page into the root category:mathematics, where it will have a better chance of spotting and classification. See also: Glossary of mathematics
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S is α-effective if the members of S have strategies s.t. no matter what the complement of S does, the outcome will be a. S is β-effective if for any strategies of the complement of S, the members of S can answer with strategies that ensure outcome a. Finite game is a game with finitely many players, each of which has a finite set of strategies.
Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists.
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A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science. Some just say, "mathematics is what mathematicians do". [166] [167] A common approach is to define mathematics by its object of study. [168] [169] [170 ...