How can I prove this proposition?
Let $(a_n)$ be a sequence. If $(|a_n|)$ is convergent then $(a_n)$ has a convergent subsequence.
If $(|a_n|)$ converges to $L$ then $\forall \epsilon>0, \exists n_0 \in \mathbb{N}$ where $n>n_0 \implies ||a_n|-L|<\epsilon$.
I got stuck here.