Axiom:Axiom of Choice/Formulation 1

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Axiom

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

$\displaystyle \forall s: \left({\varnothing \notin s \implies \exists \left({f: s \to \bigcup s}\right): \forall t \in s: f \left({t}\right) \in t}\right)$

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


Also see


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