Prove the set $K = \{\frac{1}{n} \mid n\in \mathbb{N}\}\cup \{0\}$ is compact.
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.