Metric on natural numbers united with infinity can anyone give me an example for the following metric $d$?
Let $\Omega = \mathbb{N}_+ \cup \{ \infty \}$ and $d$ be a metric such that all points $n \in \mathbb{N}_+$ are isolated w.r.t. $d$ and $\lim_{n \rightarrow \infty} d(n,\infty) = 0$.
Thank you very much!

Hint: A rough idea, here, is to treat each $n$ like $\frac1n.$ What can we treat $\infty$ like to get the desired property?
