1. The problem statement, all variables and given/known data Prove that the supremum is the least upper bound 2. Relevant equations 3. The attempt at a solution Proof: let x be an upper bound of a set S then x>=supS (by definition). If there exists an upper bound y and y<=SupS then y is not an upper bound (contradiction) therefore every upper bound is greater than SupS so SupS is the least upper bound. Is that proof correct? Thank you.