It's not an axiom in itself. I think it's a consequence of the axiom of Replacement (the image under a function of a set is a set). BICBW. --CH
(PeterTaylor) Ah. I was understanding "take an item" to mean that given a non-empty set S you can present an element x in S. I've always understood Choice in terms of computability, since constructionism seems to be the issue.
If you have an infinite number of Sets of stuff, you might not be able to. The AxiomOfChoice says you can, but it is just an Axiom? - you can get perfectly consistent set theories by assuming its converse. CategoryMaths