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He told us he could of course change the parameters which he will of the proofs we have been working on so I'm testing out some cases but I want to make sure i'm doing it right.

Here is an example of a proof the boook had:

http://suprfile.com/src/1/3qaagxh/Untitled-1%20copy.jpg [Broken]

Now where he has the statement: "If a and b are rational numbers...."

I'm changing that to:

"If a and b are integers...."

and now here is my proof, i think its correct but I have to make sure.

If a and b are integers, b != 0, and r is an irrational number, then a+ br is irrational.

Proof by Contradiction:

Suppose not. Suppose that a and b are integers, b != 0, and r is an irrational number such that a+br is rational. We must obtain a contradiction.

Since a, b are integers and a + br are rational, a+br = m/n for some integers m, n with n != 0.

Then

a + br = m/n

br = m/n - a

r = (m-an)/bn

where (m-an) and (bn) are integers since m, a, n, and b are integers, and bn is nonzero since b is nonzero. Therefore, r is rational, contradicting that r is irrational.

Thanks!

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# Homework Help: Slight deviation of proof, would it be correct for integers? Review for exam!

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