Let $\displaystyle S$ and $\displaystyle T$ be non-empty bounded subsets of $\displaystyle \mathbb{R}$, and suppose that for all $\displaystyle s \in S$ and $\displaystyle t \in T$, we have $\displaystyle s \leq t$.

Prove that supremum of $\displaystyle S \leq$ infimum $\displaystyle T$.