Mathematics is shit

Just look at these ugly swatches of code:
http://www.cse.unt.edu/~idl99/Proceedings/ahn/img50.gif
http://www.cse.unt.edu/~idl99/Proceedings/ahn/node8.html

That is what you get, when programming immitates math. Even Java and PHP looks beautiful compared to that. Mathematics should be banned as a harmful and obfuscated teaching.

>>170
http://en.wikipedia.org/wiki/Continuum_hypothesis
CH is independent of ZFC.
Like CH, GCH is also independent of ZFC, but Sierpiński proved that ZF + GCH implies the axiom of choice (AC), so choice and GCH are not independent in ZF; there are no models of ZF in which GCH holds and AC fails.
Kurt Gödel showed that GCH is a consequence of ZF + V=L (the axiom that every set is constructible relative to the ordinals), and is consistent with ZFC. As GCH implies CH, Cohen's model in which CH fails is a model in which GCH fails, and thus GCH is not provable from ZFC

http://en.wikipedia.org/wiki/Axiom_of_choice#Independence
Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model (the constructible universe) which satisfies ZFC and thus showing that ZFC is consistent. Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF¬C (ZF with the negation of AC added as axiom) and thus showing that ZF¬C is consistent. Together these results establish that the axiom of choice is logically independent of ZF.