axiom of choice
Date: 1942 an axiom in set theory that is equivalent to Zorn's lemma: for every collection of nonempty sets there is a function which chooses an element from each set

New Collegiate Dictionary. 2001.

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  • Axiom 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 …   Wikipedia

  • axiom 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… …   Universalium

  • axiom 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. * * * axiom of choice,… …   Useful english dictionary

  • axiom of choice — noun One of the axioms in axiomatic set theory, equivalent to the statement that an arbitrary direct product of non empty sets is non empty …   Wiktionary

  • Axiom of Choice (band) — Axiom of Choice is a world music group of Iranian émigrés who perform a fusion style incorporating Persian classical music and Western music. Led by Loga Ramin Torkian who plays a variant of a guitar of his own invention that is fretted to play… …   Wikipedia

  • Axiom of choice (disambiguation) — Axiom of choice may refer to:*Axiom of choice, an axiom of set theory *Axiom of Choice (band), a world music group of Iranian émigrés …   Wikipedia

  • Axiom of countable choice — The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory, similar to the axiom of choice. It states that any countable collection of non empty sets must have a choice function. Spelled out, this means… …   Wikipedia

  • Axiom of determinacy — The axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two person games of length ω with perfect information. AD states that every such game in… …   Wikipedia

  • Axiom of global choice — In class theories, the axiom of global choice is a stronger variant of the axiom of choice which applies to proper classes as well as sets. Statement The axiom can be expressed in various ways which are equivalent: Weak form: Every class of… …   Wikipedia

  • Axiom of regularity — In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo Fraenkel set theory and was introduced by harvtxt|von Neumann|1925. In first order logic the axiom reads::forall A (exists B (B in A)… …   Wikipedia

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