Category:Examples of Use of Axiom of Choice

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This category contains examples of use of Axiom:Axiom of Choice.

For every set of non-empty sets, it is possible to provide a mechanism for choosing one element of each element of the set.

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

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

Pages in category "Examples of Use of Axiom of Choice"

The following 68 pages are in this category, out of 68 total.