Let $A$ be a nonempty bounded subset of $\mathbb R$ and let $B$ be the set of all upper bounds for $A$. Prove that $\sup A=\inf B$

Let $A$ be a nonempty bounded subset of $\mathbb R$ and let $B$ be the set of all upper bounds for $A$. Prove that $\sup A= \inf B$. Can someone please help me? I'm very confused as to what to do.