1. The problem statement, all variables and given/known data Show that if a < b + ε for every ε>0 then a ≤ b 2. Relevant equations I am not sure if this is a right way to do it? I just want to know if it does make sense 3. The attempt at a solution proof. a < b + ε → if a is bounded above by b+ε then b is the least upper bound for a. which means a ≤ b. ε is the upper bound of a since b≤ε.