axiom of choice (selection)
1Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …
2axiom of choice — Math. the axiom of set theory that given any collection of disjoint sets, a set can be so constructed that it contains one element from each of the given sets. Also called Zermelo s axiom; esp. Brit., multiplicative axiom. * * * ▪ set theory… …
3Choice function — A choice function (selector, selection) is a mathematical function f that is defined on some collection X of nonempty sets and assigns to each set S in that collection some element f(S) of S. In other words, f is a choice function for X if and… …
4Luce's choice axiom — DOI and citation tidying.In probability theory, Luce s choice axiom, formulated by R. Duncan Luce (1959), states that the probability of selecting one item over another from a pool of many items is not affected by the presence or absence of other …
5Finite set — In mathematics, a set is called finite if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. (The value n = 0 is allowed; that is, the empty set is finite.) An infinite set is a set which is… …
6metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …
7Paracompact space — In mathematics, a paracompact space is a topological space in which every open cover admits a locally finite open refinement. Paracompact spaces are sometimes also required to be Hausdorff. Paracompact spaces were introduced by Dieudonné (1944).… …
8Game theory — is a branch of applied mathematics that is used in the social sciences (most notably economics), biology, engineering, political science, computer science (mainly for artificial intelligence), and philosophy. Game theory attempts to… …
9Arthur Rubin — Arthur Leonard Rubin (born 1956) is an American mathematician who has earned a place among the five top ranked undergraduate competitors (who are themselves not ranked against each other) in the William Lowell Putnam Competition four times… …
10Binomial coefficient — The binomial coefficients can be arranged to form Pascal s triangle. In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the… …
