Let E?R be defined by E={1/n :n?N}. Prove the following byappealing only to the definition of compactness, without using theHeine-Borel theorem.(a) Prove that E is not compact. In other words, Let \( E \subset \mathbb{R} \) be defined by \( E=\left\{\frac{1}{n}: n \in \mathbb{N}ight\} \). Prove the following by appealing only to the definition of compactness, without using the Heine-Borel 1 answer