According to Wikipedia, Zermelo formulated the axiom of choice.

I think it makes sense though; if I (claim to) have a thing, I should be able to choose/pick/select/point-to it (seems to be almost[?] tautological).

"Say you are playing a game that needs you to pick a real number. If you choose a computable real number, you lose the game. If you choose a real number that is not computable, which the majority real numbers are, then you win. You can imagine yourself choosing a non-computable real number, and winning the game, if you build in the axiom of choice. But in the real world version of the game you will never have enough time or space to non-ambiguously specify this infinitely precise real number which has an infinite amount of non-compressible information (see Kolmogorov complexity)."-Khatchig, from "Digital Physics" (the movie)