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That wasn't my point. Rather, I was suggesting that proofs by contradiction can easily be in error (because if you make an error, you have a good chance of even
by CurtMonash 14y ago
That wasn't my point. Rather, I was suggesting that proofs by contradiction can easily be in error (because if you make an error, you have a good chance of eventually getting to your contradiction).
Anyhow, when I did mathematics, I didn't run into people caring about proof by contradiction vs. direct proof. However, I did occasionally run into a preference for constructive vs. non-constructive proofs. E.g., my thesis used a prior result that included a funky existence proof, and my adviser pushed me to find an alternate proof that was directly constructive.
- raverbashing 14y agoOh yes, I had understood that "proofs by contradiction can easily be in error" but I suppose that's because people try the contradiction proof first, because it "should be easier" And of course, constructive proofs are usually more complicated, in terms of proof structure as well as 'where to go and how to get there'
- CurtMonash 14y agoMy comment was based on a more precise point, namely that #3 in the process below is very natural: 1. Assume the theorem is false. 2. Make some calculations based on that assumption. 3. Eventually, make an error. 4. Pursue that error to a contradiction. 5. Claim victory.