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!