Prove that $f_n(x) → f(x)$ uniformly on $E$ as $n →∞.$

Let $E ⊂ \mathbb{R}$ be a compact (i.e., closed bounded) set of real numbers. Suppose $\{f_n\}$ is a sequence of real-valued continuous functions which converges pointwise on $E$ to a function $f$ that is also continuous on $E.$ Suppose further that the sequence $\{f_n\}$ is monotonic: $f_{n+1}(x) ≤ f_n(x)$ for all $x ∈ E$ and all $n = 1,2,....$

(a) Prove that $f_n(x) → f(x)$ uniformly on $E$ as $n →∞.$

(b) Show by example that the hypothesis of compactness is essential.

I need to show that $||f_n - f||_{\infty}$ tends to $0$ as $n$ tends to $\infty$ but I am not really sure how to do this. Advice would be awesome. Thanks.