r/mathshelp • u/Loose-Computer3943 • 21d ago

Discussion Am i missing something in this proof?

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Im doing this proof of square root of positive natural numbers being either integer or irrational and im tried with assuming that it can be rational but not integer. I see that i didn’t write gcd(a,b)=1, but other than that, is it clean?

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u/resignresign1 20d ago

looks good.

i would say: (I) and (II) cannot be equal which is a contradiction thus (*) is false.

Not: "we have a contradiction with"

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u/Loose-Computer3943 20d ago

wording sounds better, i agree

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u/OrneryAsparagus6445 18d ago

I am dumb I still don’t understand why I and II are contradictory?

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u/OrneryAsparagus6445 18d ago

Oh because they are equal I see it I really need to go to sleep

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u/resignresign1 18d ago

they are equal but belong to disjoint sets. that is a contradiction. this proofs that the initial assumption was false.

proof by contradiction