calculus - Prove: If $lim_{nrightarrowinfty}|a_n| = 0$, then $lim_{nrightarrowinfty}a_n = 0$

Using the squeeze theorem, prove the following:

If $\lim_{n\rightarrow\infty}|a_n| = 0$, then $\lim_{n\rightarrow\infty}a_n = 0$.

Let $f(x) = |a_n|$. Let $g(x) = a_n$ such that $\forall x : g(x) \leq f(x)$. How do I continue this proof using the squeeze theorem? I want to construct a function $h(x)$ that lies in between those two functions.

Answer

Hint : $-|x|\le x\le |x|{}{}{}{}{}{}$