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An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
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Non-constructive existence proofs without AC?
Hi everyone,
This is a question I have been asking from long, but none of my colleagues could ever answer me:
It is a well-known fact that the axiom of choice (AC) allows one to prove the existence …