1. The problem statement, all variables and given/known data If A and B are bounded sets, then A U B is a bounded set. (Prove this statement) 2. Relevant equations Definition of Union is a given. A set A is bounded iff there exists some real value m such that lxl < m for all element x found in A. 3. The attempt at a solution This makes sense to me. If set A is bounded by M and set B is bounded by N, then A U B will be bounded by which value is higher. I have to keep in mind that the definition of a bounded set has the "iff" term. My attempt (this is quite odd looking to me, I don't know how to make it more straightfoward) Let x exist in A. Then that means there is a value m where m>lxl by definition of a bounded set. Let y exist in B. Then that means there is a value n where n>lyl by definition of a bounded set. Thus, x and y exist in A U B by definition of union. We know lxl and lyl are < whichever value of m or n is the larger of the two. Thus, A U B is a bounded set. The bolded step seems oddest, but critique on any part of the proof is welcome. Help!