In proofs like prove sqrt(2) is irrational using proof by contradiction it typically goes like-We assume to the contrary sqrt(2) is rational where sqrt(2)=a/b and b≠0 and a/b has been reduced to lowest terms. I understand that at the very end of the arrive we arrive at the conclusion that it has not been reduced to lowest terms which leads to a contradiction. But what allows me assume a\b has been reduced to lowest terms? For all I know a/b could have not been reduced at the very beginning.(adsbygoogle = window.adsbygoogle || []).push({});

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# Prove sqrt(2) is irrational

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