http://en.m.wikipedia.org/wiki/Zorn's_lemma http://en.m.wikipedia.org/wiki/Zorn's_lemma Minor major nitpick: Axiom of (Uncountable) Choice (AUC) is controversi

http://en.m.wikipedia.org/wiki/Zorn's_lemma http://en.m.wikipedia.org/wiki/Zorn's_lemma Minor major nitpick: Axiom of (Uncountable) Choice (AUC) is controversial. It isn't intuitive, but it is independent from the intuitive axioms, which means that you don't have to accept it, and if all you care about is things that might ever be computable during the existence of the Universe, you never need AUC, and AUC never tells you anything useful since it is nonconstructive in the worst way. (It doesn't even say, like NP does in computing, that if you brute-force, you can solve any problem to any desired level of accuracy). AUC just asserts an answer exists. The interestingness is in knowing what other statements are equivalent to it , but it is and forever will be confined to purely abstract math (really! Unlike RSA, there will provably NEVER be a computational or physical application in the accessible world of countable infinities.)