1. The problem statement, all variables and given/known data Let x and y be real numbers. Prove that if x =< y + k for every positive real number k, then x =< y 3. 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.