What's the difference? Uncountable sets does not respect out intuition about countable sets. AC is independent from ZF, meaning it doesn't matter for any appli

What's the difference? Uncountable sets does not respect out intuition about countable sets. AC is independent from ZF, meaning it doesn't matter for any application to anything in the Universe, including physics or computing. Theory of uncountable objects is a game to play with symbols, the only thing "real" about them is that they are the firm boundary between the potentially reachable and the infinite void. The name itself conveys an important truth.