$O(n^2)$ and $O(n\log n)$ exercise
Consider for Al $f_{Al} \in O(n \log n) $:
$$f_{Al}(n)=\begin{cases}n\log n, &amp; \text{ when }n\lt 100 &amp; \\
n  , &amp;\text{ when }n \geqslant 100\end{cases}$$
For Bob let's take $f_{Bob}(n) \in O(n^2)$
$$f_{Bob}(n)=\begin{cases}n, &amp; \text{ when }n\lt 100 &amp; \\
n\log n  , &amp;\text{ when }n \geqslant 100\end{cases}$$
Note also, that since for asymptotic relations it is only important what happens from some number to infinity, then Bob and Al are arguing in vain.