Find an example of a function $f$ such that satisfies: $$\forall_{\varepsilon>0} \ f(n)=O(n^{1+\varepsilon})$$ but not $$f(n)=O(n)$$
I had been thinking about it for an hour and still can't find it. Can anybody help?
Find an example of a function $f$ such that satisfies: $$\forall_{\varepsilon>0} \ f(n)=O(n^{1+\varepsilon})$$ but not $$f(n)=O(n)$$
I had been thinking about it for an hour and still can't find it. Can anybody help?
Hint: $\log n = O(n^{\epsilon})$ for all $\epsilon > 0$.