# Infinum of exponential series

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.

• Take $n>\log_\alpha (\varepsilon )$, then $a^n<\varepsilon$. – Surb Sep 16 at 14:53
• Thank you sir. I'm an idiot. – user962158 Sep 16 at 15:01