Let $x,\,y \in \mathbb{R}$ such that $x > 1, y > 0$. Using reductio ad absurdum prove $ \exists n \in \mathbb{N}\colon y < x^n $ Suggestion: if $\varepsilon > 0$ is small and $n\in \mathbb{N}$, then there exists $n$ for which $x^n + \varepsilon < x^{n+1}$.
Thanks in advance.