Show that $\mathbb{Z}_p$ = $\varprojlim_n \mathbb{Z}/p^n$ is the completion of $\mathbb{Z}$ with respect to the metric $(x, y) \rightarrow \|x-y\|_p$, i.e, the p-adic metric.
I've tried doing this with cauchy sequences, but I don't think it's right. I feel like this is pretty standard. Is there a way to do it with imbeddings?