stringzoffury wrote:Let x and y be real numbers. Prove that if x <= y + b for every positive number b, then x <= y.
Proof by contradiction might be a useful way to proceed. Assume that x is less than or equal to y for every positive value b, but also that x is greater than y. Where does this lead?
If you prefer using a different technique, kindly please reply showing your progress thus far. Thank you.