"The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes."


"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" 


What are people's opinions on choice?


Proofs involving choice are often delightfully unenlightening or even paradoxical, but it does have uses.

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The easiest way of seeing it outside of set theory is in linear algebra. The AC is logically equivalent to saying "every vector space has a basis".

AC can be used to construct non-measurable sets, which leads to the Banach-Tarski paradox, something that is well worth looking up!

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