I am reading about big O notation on wikipedia, and it say the following;
For any $k>0$ and $c>0$, $O(n^{c}(\log n)^{k})$ is a subset of $ O(n^{c+\epsilon })$ for any $\epsilon >0$, so may be considered as a polynomial with some bigger order.
I am struggling to see this. In particular, I can not see how this would hold for every $\epsilon>0$. It is clear that it holds for $\epsilon\geq k$, but how would it be shown for $0<\epsilon<k$?
Thanks