The axiom of choice is wrong

dupe: https://news.ycombinator.com/item?id=13571315

There are counter intuitive consequences of the Axiom of Choice. There are counter intuitive consequences without choice [1]. There are weaker versions of the Axiom of Choice, like countable choice. Here’s a statement that is equivalent to the Axiom of Choice: The product of non-empty sets is non-empty. It seems clear, naively speaking, that the product of non empty sets should be non empty and believing this means you accept the Axiom of Choice.

Whatever you decide to believe with regard to the Axiom of Choice you end up with weird stuff happening when dealing with uncountable sets. The intuition with dealing with countable sets does not extend to uncountable sets in many cases.

[1]. https://mathoverflow.net/a/22935

When something is neither obvious (like, say, the axioms of planar geometry) nor subject to geometric or mathematical proof (like, say, the infinitude of primes) or experimentation (the atomic theory of matter), it's interesting at a philosophical level to discuss why we should believe P or not-P (or neither or both, I suppose)

Personally, since it appears that there's no feasible physical scenario which would point to the "truth" of ZFC over ZF+~C, I have trouble understanding how it's useful to debate the point. I can tell you what happens in the thought experiment with the infinite number of prisoners: according to GR, since they are infinitely massive they collapse into a black hole no matter the average density of the sphere enclosing all the prisoners. Thus, the axiom of choice is disproven :-P