(Taking a Algorithms course now, so I might get it wrong, if so, RIP to my finals in a few weeks)

I think O notation represents the upper bound, so a complexity of N can also be said as O(N^2) or O(N^3), but that isn't particularly useful.

In other words, if f(x)/g(x) < inf when x->inf, then f(x) = O(g(x)).

Then there's omega-notation (lower bound, f(x)/g(x) > 0) and theta-notation (both lower and upper bound, 0 < f(x)/g(x) < inf).