Solution
= Solution
By the <Heine-Borel theorem>, a subset of $\mathbb R$ is compact exactly when it is closed and bounded. Consequently the compact <interval>[intervals] are
$$
\boxed{[u,v]\quad\text{with finite }u\leq v,}
$$
including singleton <interval>[intervals]. The empty <interval> is compact too, if included in the <interval> convention. Nonempty open, proper half-open, and unbounded <interval>[intervals] are not compact.