I ran into the following notation issue:
Suppose that I have two functions $f$ and $g$ and I know that $\displaystyle \lim_{n \rightarrow \infty} \frac{f(n)}{g(n)} = c$ for some $1 < c < \infty$.
I want to express that $f$ is an asymptotic upper bound for $g$, but saying $g(n) = O(f(n))$ is worthless because coefficients are dropped.
Is there a way to express this upper bound more tersely than the limit expression above? In other words is there any "order-O-like" notation for expressing this?
Clarification: I'm not looking for any of the symbols here. The question may be too pedantic.