## LolWolf Group Title 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. one year ago one year ago

1. mukushla Group Title

but for n=2 ?

2. mukushla Group Title

that needs another complete proof :)

3. LolWolf Group Title

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

4. mukushla Group Title

lol

5. LolWolf Group Title

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 $$n<p<2n$$, thus our original statement contradicts Bertrand's postulate. Proof for the postulate here: http://en.wikipedia.org/wiki/Proof_of_Bertrand%27s_postulate

6. mukushla Group Title

thats interesting too...

7. LolWolf Group Title

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/)

8. zzr0ck3r Group Title

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

9. mukushla Group Title

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

10. zzr0ck3r Group Title

thats the one.

11. LolWolf Group Title

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

12. zzr0ck3r Group Title

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

13. zzr0ck3r Group Title

lol

14. LolWolf Group Title

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

15. mukushla Group Title

man diophantine equations is my favorite topic :)

16. zzr0ck3r Group Title

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

17. LolWolf Group Title

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...