Is this a proof by contradiction (we suppose that root 2 can be expressed as the ratio of two coprime integers and then find that they're not actually coprime) or a proof by infinite descent (the fraction can be simplified forever so it can't be rational)? Is there any way to prove it without supposing at first that it is rational?
Proof that sqrt(2) is irrational Watch
- Thread Starter
- 10-11-2008 17:55
- 10-11-2008 17:58
The contradiction is shown by infinite descent. There are other methods, such as: http://en.wikipedia.org/wiki/Square_...#Another_proof and the method below that.
P.S. "infinite descent" is a cool sounding phrase. There should be a film or band with that title.
- 10-11-2008 18:00
yeah its a proof by contradiction!
- 10-11-2008 18:16
Actually, its proof by cases. According to a book I have called how to prove it.