- #1
RJLiberator
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Homework Statement
For each of the relations defined on ℚ, either prove that it is an equivalence relation or show which properties it fails.
x ~ y whenever xy ∈ Z
Homework Equations
The Attempt at a Solution
Here's my problem: I am starting off the proof with the first condition of reflexivity.
Now, do I let x ∈ ℚ ? I would think so, if that is the case, then x can be 2/3.
So xx is thus 4/9 which does not exist in the integers.
Thus, the proof would fail.
But I think I am missing something here. Did I do this right or am I making a fatal error by suggesting that x can be any ℚ?