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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.

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

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