1. The problem statement, all variables and given/known data If b>a, find the infimum of b - a for arbritrary b,a. 2. Relevant equations - 3. The attempt at a solution So this is for a darboux sum but I'm stuck on proving that 0 is the inf. It seems really easy but I can't seem to think straight. First thing is 0 is a lower bound of b - a. b - a > 0 b > a Next is to prove it's the greatest lower bound. I tried to do this by supposing x > 0 is the greatest lower bound and find some contradiction but I can't figure it out.