(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove: For every rational number z, there exists irrational numbers x and y such that x + y = z.

2. Relevant equations

by definition, a rational number can be represented by ratio of two integers, p/q.

3. The attempt at a solution

Is there a way to do this by contraposition?

Would the contraposition be, For all rational numbers x and y, there does not exist an irrational number z such that x + y = z? I can handle from there, but I don't think my contraposition is correct.

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# Homework Help: For every rational number, there exists sum of two irrational numbers

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