TITLE: What is the Axiom of choice
QUESTION [0 upvotes]: I was learning Set Theory for fun and I came across something called the axiom of Choice, 
What is the axiom of choice?

REPLY [0 votes]: The axiom of choice says that there is a set of all left socks.  If the two socks in each pair are indistinguishable, then there is no rule of deciding which sock in each pair is to be considered the left sock.  The axiom of choice says that there is a set that contains exactly one member of each pair (and if there is one such set, then it follows that there are many).
One form of the axiom of choice says that in every set of pairwise disjoint non-empty sets, there is a set that contains exactly one element of each of them.
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