If the numbers in one set are all larger than those in another set, are there numbers in between?

Question

Let $S, R \subseteq \mathbb{R}$ be sets of real numbers such that for every $s \in S$ and $r \in R$, $s<r$. How can one prove that there exists some real number $t$ satisfying $s <t <r$ for all $s\in S$ and $r \in R$?