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Prove sqrt(2) is irrational 
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#1
Nov2912, 08:33 PM

P: 232

In proofs like prove sqrt(2) is irrational using proof by contradiction it typically goes likeWe 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.



#2
Nov2912, 08:35 PM

P: 232

oops I think I posted it in the wrong section.



#3
Nov2912, 08:48 PM

P: 181

But you see why proving the special case is enough to cover the nonreduced case as well, don't you? This small step ("no reduced fraction, so no nonreduced fraction either") is so obvious that it's not even mentioned. At least I've never seen it being spelt out explicitly. 


#4
Nov2912, 09:15 PM

P: 232

Prove sqrt(2) is irrational
Oh wow now I get it. I never thought of it like that. So basically the proof is saying that sqrt(2) is reduced to lowest terms and sqrt(2) is not reduced to lowest terms which means that it rules out any possibility of it being written as a fraction.Thus its irrational.



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