I have been reading this tutorial on time complexity, and I am a bit puzzled on its explanation of big $O$ notation. It writes:
$O(g(n)) = $ { $f(n)$ : there exist positive constants $c$ and $n_0$ such that $0 \leq f(n) \leq c*g(n)$ for all $n > n_0$.
The way I understand it, $c*g(n)$ denotes $c$ multiplied by $g(n)$. If this is the case, then how does the above expression specify time, and not just that $c*g(n)$ is greater than $f(n)$? Or am I incorrect, and this is some notation I don't understand? My understanding of time complexity is very rudimentary, so forgive me if this is just a stupid mistake on my part.