Infinum of exponential series

27 Views Asked by At

Fix $\alpha \in (0,1)$. Determine $\inf(B)$ for $B$ = $\{a^{n}:n\in N \}$

How do I show that $\alpha^{n} < \epsilon$?

I feel like this is true: $\epsilon > \frac{1}{n} > \alpha^{n}$ but I don't understand how to get here. We've only used Archimedean property so far.