Proof by contradiction

  1. I never understand the proof by contradiction, because somewhere in the middle I always lost myself.

    In this https://www.physicsforums.com/showthread.php?t=523874 there's an example of proof by contradiction.


    We assume that if n^2 is odd than n is odd. This means that if n^2 is even, n can be odd or even. How can I proof a contradiction if n is even? It doesn't tell me nothing.
     
  2. jcsd
  3. No, n^2 even implies n even. You are trying to show that if n^2 is odd, then n must be odd. So you assume that it's not true, i.e. if n^2 is odd then n is not necessarily odd. The only other choice is n is even. So suppose n^2 is odd and n is even. The result above is that if n is even then n^2 is also even. This contradicts the original assertion that n^2 was odd so it can not be true that if n^2 is odd, then n is even. The only choice left is that if n^2 is odd, then n is odd.
     
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