Let x and y be real numbers. Prove that if x =< y + k for every positive real number k, then x =< y
The Attempt at a Solution
x =< y + k
-y + x =< k
since k is positive, the lowest value it can take doesn't include 0: -y + x < 0
x < y
So I get x < y from x =< y + k and not the required x =< y. Am I right or I'm screwing up somewhere? Thanks for your help.