I'm studying for Real Analysis and I can't understand the application of Lemma for covering sets numbers.
Decide whether cover $\zeta$ of the space X has a covering number. If so, find the set of all covering numbers for $\zeta$. $X=(-\infty,1)$ and $\zeta=\{{G_n\}}$ where $G_n=(n^2,1)$ for all $n$ belonging to natural numbers
If anyone could please explain the mechanics behind finding this (I know this means that $\inf\{{\delta(x): x {\rm\ belongs\ to\ }X\}}=0$ , but how do I find that?) I would be very grateful.