I have a trivial question which is rather obvious but I need a short and concise proof. I need a constructive proof and not just a counterexample. I have constructed a proof by contradiction myself but I think there are shorter ways of doing this. I would be greatful for any help!

I want to show that the implication:

(x-y) > e implies (x-y) => 0

cannot be true for any e<0.

x any y are two scalar with support on the real line