Does $n^\varepsilon \gt n\log n$ for $\varepsilon \gt 1$?
I'm pretty sure I heard once the lecturer stating this, is that true?
2026-04-25 13:29:16.1777123756
Does $n^\varepsilon \gt n\log n$ for $\varepsilon \gt 1$?
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This is equivalent to $n^{\varepsilon -1}>\log n$. Now, it's a basic result that $$\log n=o(n^{\alpha})\quad\text{for all}\enspace\alpha>0.$$ So it's true if $n$ is large enough.