/sci/ - Science & Math

>>11714637
I'm gonna give a really shitty answer since it doesn't look like anyone's giving a good one.

Assume that the axiom of choice isn't trivial. That is, it guarantees the existence of at least one choice function which, without the AoC, cannot be shown to exist (which in particular means it can't be constructed).
Then this function is a set whose existence is implied by AoC but cannot be constructed.

Of course, the whole non-triviality thing is the independence of choice from ZF.