I'm trying to understand the concepts underlying the O-notation.
The formal definition is:
$ O(g(n)) = \{ f(n) \textrm{ such that there exist positive constants }c\textrm{ and }n_{0} \textrm{ such that }0 \leq f(n) \leq cg(n) \} $
Then there is this notion of $f(n) = O(g(n))$ meaning $f(n) \in O(g(n))$.
What I don't understand is the reason why we use this set notation. I'm not sure to understand the actual content of this set $O(n)$.
Thanks for your help! I can be more precise if you want.