# Proving properties of supremum

$$\sup(A + B) = \sup A + \sup B$$
Let $$E$$ be a set of real numbers that is nonempty and bounded above. If $$F \subset E$$, then $$\sup F \le \sup E$$.
401.2A Proof using supremum
Matthew Salomone
401.1X Finishing supremum proof
Matthew Salomone