Does anyone have any (hysterical) ridiculously-overblown proofs of simple statements? I'll give an example:
$\sqrt[n]{2}$ is irrational for all $n2\in \mathbb{Z}$
Proof:
Suppose $\sqrt[n]{2}=\frac{p}{q}$ for some $p,q\in \mathbb{Z}$, then
$$
2=\frac{p^n}{q^n} \implies\
2q^n=q^n+q^n=p^n
$$Contradicting Fermat's Last Theorem.
I'd love to see some more of these, haha.

Question

Does anyone have any (hysterical) ridiculously-overblown proofs of simple statements? I'll give an example:
$\sqrt[n]{2}$ is irrational for all $n>2\in \mathbb{Z}$
Proof:
Suppose $\sqrt[n]{2}=\frac{p}{q}$ for some $p,q\in \mathbb{Z}$, then
$$
2=\frac{p^n}{q^n} \implies\
2q^n=q^n+q^n=p^n
$$Contradicting Fermat's Last Theorem.
I'd love to see some more of these, haha.

anonymous · Answer

but for n=2 ?

anonymous · Answer

that needs another complete proof :)

anonymous · Answer

Yeah, of course. Haha, it seems that Fermat's isn't strong enough to prove that...

anonymous · Answer

lol

anonymous · Answer

Another interesting proof: There is an infinitude of primes: We begin by stating some large number $n$ over which there exists no primes. If $n>1$, there must exist a prime $p$ such that $n http://en.wikipedia.org/wiki/Proof_of_Bertrand%27s_postulate

anonymous · Answer

thats interesting too...

anonymous · Answer

Haha, it's sort of absolutely ridiculous... I'm trying to come up with these as I finish up some homework... but I'm having a hard time. (Although the first one is from http://rjlipton.wordpress.com/2010/03/31/april-fool/)

zzr0ck3r · Answer

I saw another good one for infinite primes but its been a while.

anonymous · Answer

Proof of the Infinity of the Prime Numbers this is simple but i like it http://www.hermetic.ch/pns/proof.htm

zzr0ck3r · Answer

thats the one.

anonymous · Answer

A proof that $\nexists x, y \in \mathbb{Z} \text{ s.t. }x^3+113y^3=1$ http://books.google.com/books?id=YXDYKJvZY0QC&pg=PA111&lpg=PA111&dq=R+Finkelstein+and+H+London,+On+D.+J.+Lewis%27s+equation&source=bl&ots=YiyOhNRaLi&sig=JmtUPqakWZ5Mf4tqab8UMzQ_ecE&hl=en#v=onepage&q=R%20Finkelstein%20and%20H%20London%2C%20On%20D.%20J.%20Lewis%27s%20equation&f=false

anonymous · Answer

Oh, yeah, the Euclidean proof. It's nice, and pretty simple, with some extra lemmas to work from the axioms.

zzr0ck3r · Answer

http://www.cut-the-knot.org/pythagoras/index.shtml 97 proofs of pythagoreans theorem!

zzr0ck3r · Answer

lol

anonymous · Answer

I just want, as they say, to 'nuke a mosquito'. With absolutely absurd proofs for simple statements.

anonymous · Answer

man diophantine equations is my favorite topic :)

zzr0ck3r · Answer

well then look up the proof for 2+2 = 4, its about 500 pgaes long.

anonymous · Answer

Haha, it actually IS. To prove that like $0\cdot m=0$ takes quite a bit of work, from axioms. Oh, and that $1 \in \mathbb{N}$, also does...