$O(2^{o(n)}) = O(2^n)$？ 2美元的力量有一点点

Question

During an NP hard problem's complexity analysis, I am stuck at this term.

$O(2^{o(n)})$

In particular:

O(2^{no(n)})+O(2^{o(n)})

I ended up at an answer $O(2^n)$ equating $O(2^{o(n)}) = O(2^n)$ by considering the worst case for the $o(n)$ as $n$.

Any push forward with a short proof would be very helpful.

Answer 1

The worst case of o(n) is not n . The little-o is interpreted as asymptotically less than n .Hence, if f(n) is in o(n) , then lim(f(n)/n)) when n goes towards infinity is equal to 0 .Example of o(n) functions are sqrt(n) and log(n) .