1. The problem statement, all variables and given/known data Let A be a nonempty set of real numbers which is bounded below. Let -A be the set of all real numbers -x, where x is in A. Prove that inf A = -sup(-A). 2. Relevant equations Definitions of upper bound, lower bound, least upper bound, and least lower bound. 3. The attempt at a solution Here's what I have so far: Almost there! I just need to derive a contradiction on my assumption that gamma is an upper bound for -A.