what's the name for asymptotic without multiplier?

Question

(In combinatorics) When talking about asymptotic behaviour of a function. Seemingly we have already decided the multiplier. For example, we would say $\binom{n}{2}$ is asymptotically $1/2*n^2$, but not $n^2$. My question is, what should we say about a function $f$ if we only know $\lim \frac{f}{n^2}$ is bounded away from $0$ and $\infty$, but don't know that exact number?

Answer 1

Perhaps the big O notation is what you are looking for?

It's a notation that "ignores the constant factor". By definition, $f\in O(g)$ if there exists some constant $C$ such that $f(x)<C\cdot g(x)$ for all large enough values of $x$. For example, $$an^2+bn+c\in O(n^2)$$ no matter what the particular constants $a,b,c$ are.