- 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.
axiom of choice
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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 (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 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
Choice (disambiguation) — Choice consists of the mental process of thinking involved with the process of judging the merits of multiple options and selecting one of them for action. Choice may also refer to: Contents 1 Mathematics 2 Media 3 Other 4 … 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
