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Why is it that whenever we wish to prove a negative claim that it is often a good approach to construct a proof by contrdiction

atifcppprogrammer
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  • What other obvious technique would there be? – siegehalver Jun 13 '17 at 00:36
  • Whenever we wish to prove anything, it is a good approach to use one of the standard proof techniques. That you have noticed in your own experiences several examples of proofs by contradiction being used to prove negative claims may just be observation bias. Many of those could just as easily have been worded as proof by contraposition or even had direct proofs written. Examples are often written in textbooks or specific solutions are highlighted in homeworks to get you used to various techniques, but I disagree that there is much of any correlation here outside of instructional choices. – JMoravitz Jun 13 '17 at 00:41
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    Suppose it weren't. Then we would certainly never see important theorems proved using non-constructive arguments and contradiction. But such theorems occur frequently in mathematics. Thus the hypothesis must be false, and contradiction arguments must be useful. – Chris Jun 13 '17 at 00:49
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    @Chris If your comment wasn't funny I wouldn't have upvoted it. But I did! – Bram28 Jun 13 '17 at 01:29

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For example to prove that $A\ne B $, it is easier to suppose that $A=B $ because with equality, we can go further than with inequality. we can square, integrate...

hamam_Abdallah
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