Axiom-of-choice definition

An axiom of set theory asserting that for a nonempty collection A of nonempty sets, there exists a function that chooses one member from each of the sets including A .
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(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty.
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Other Word Forms

Noun

Singular:
axiom-of-choice
Plural:
axioms of choice