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?
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Proof that sqrt(2) is irrational watch
- Thread Starter
- 10-11-2008 16:55
- 10-11-2008 16:58
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 17:00
yeah its a proof by contradiction!
- 10-11-2008 17:16
Actually, its proof by cases. According to a book I have called how to prove it.