The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's Lemma?

Jerry Bona

I sometimes speak to people who reject the axiom of choice, or who say they would rather only accept weaker versions of the axiom of choice, like the axiom of dependent choice, or most commonly the axiom of countable choice. I think such people should stop being silly, and realize that obviously we need the axiom of choice for modern mathematics, and it's not that weird anyway! In fact, it's pretty natural.

So what is the axiom of choice? The axiom of choice simply says that given any indexed collection of (non-empty) sets, you can make one arbitrary choice from each set. It doesn’t matter how many sets you have — you could have an uncountable number of sets. You can still make a choice from all of the sets, saying “I’ll take this element from the first set, that element from the second set, this element from the third set…” and so on.