Quote:
Do you believe that an infinite product of nonempty sets should be nonempty? Do you feel that non-measurable subsets of the reals should exist? Or games of perfect information with no winning strategy for either player? Do you believe that every set should have a well-ordering, or that any poset in which every chain has an upper bound is entitled to a maximal element? Do nonzero rings have the right to a maximal ideal? Should fields have algebraic closures? Should products of compact topological spaces be compact, and countable unions of countable sets be countable? Do you want to be able to cut a sphere up into a finite number of pieces and reassemble them, with only rigid motions, into a sphere twice as large?
It's all possible if you're pro-axiom-of-choice!
