Axiom of Choice

A set-theoretic axiom asserting that for any family of nonempty sets there exists a choice function selecting one element from each set; often abbreviated AC and independent of Zermelo–Fraenkel axioms (ZF) so that accepting it introduces nonconstructive consequences.

The principle that for any collection of nonempty sets there exists a function (choice function) selecting one element from each set; stated as an axiom in set theory to assert existence without providing a constructive rule.

The principle asserting that for any family of nonempty sets there exists a choice function selecting one element from each set; commonly abbreviated AC and taken as an axiom independent of ZF set theory.

The statement that for any family of nonempty sets there exists a function (a choice function) that selects one element from each set in the family, asserting existence of a simultaneous selection even when no explicit rule is given.