I need your help with the following statement:
Show there exist two function $f(n), g(n)$ such that meet the following definition:
$g(n) = O(f(n))$ and $f(n) \ne O(g(n))$
But don't meet the little-o definition, that is :
Not for every $\epsilon >0$ there exist $n_0 \ge 1$ such that $g(n) \le \epsilon f(n)$ for every $n \ge n_0$
I'm not sure what way should I pick here.
It seems like every "Normal" two functions which meets the first definition also meets the little-o definition.
Thanks in advance!