Re: Questions about Axiom of Choice

agapito6314@xxxxxxx wrote:
1.- It is a "pure existence" statement, that is it tells something
exists but not what it is. Is math not full of these kinds of
statements?

Modern abstract mathematics is indeed full of "pure existence" statements.

The axiom of choice differs from the other axioms of set theory in that it postulates the existence of sets not - without additional set theoretic assumptions - definably by any explicit condition; that is, we can only say that the choice function for a set A satisfies certain mathematical criteria, but can't, in terms of A, provide a condition P such that f(x) = y just in case P(x,y).

2.- Some of its implications are weird or counterintuitive. Can
someone please explain some of these?

Since weirdness and counterintuitiveness is a matter of opinion, do you have any specific implications in mind?

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.