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

Prove or disprove: ∀x ∈ R ∃y ∈ R so that xy ∈ Z.

(R denotes set of all real nuimbers, Z denotes set of all integers)

2. Relevant equations

3. The attempt at a solution

I'm not sure how to attack this question. It seems false, but I can't think of a good counterexample.

Like If I say take pi, I don't think there is any other number you could multiply pi by to make an integer, but I don't know how to formulate this into a proof that makes sense. I also thought of playing with irrationals since maybe they could provide a counter example, but I'm not sure how to prove something like this. Maybe it's just something I'm not seeing.

Can anyone help get me started? Thanks!

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# Homework Help: Proof about product of reals

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