Axiom:Axiom of Choice/Formulation 1

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For every set of non-empty sets, we can provide a mechanism for choosing one element of each element of the set.

$\displaystyle \forall s: \paren {\O \notin s \implies \exists \paren {f: s \to \bigcup s}: \forall t \in s: \map f t \in t}$

That is, one can always create a choice function for selecting one element from each element of the set.

Also see

  • Results about the Axiom of Choice can be found here.