# Definition of “eventually dominates”

What is the definition of the term "eventually dominates"? I guess it's either

• $f$ eventually dominates $g$ if for large enough $n$, $f(n) > g(n)$

or the same with $\ge$. A quick Google search didn't reveal anything.

-
Depends on the context (I could imagine it meaning either that or that $\frac{f(n)}{g(n)}$ tends to infinity). Where did you read this phrase? –  Qiaochu Yuan Oct 4 '12 at 16:23
I can't remember where I read it... actually, now I'm looking for a term that means what I said, but I'm not sure if this is right (of course, I can just define it that way, but if that's not the standard meaning I will find another term) –  Max Oct 4 '12 at 16:48
I think "eventually greater than" would be less ambiguous. –  Qiaochu Yuan Oct 4 '12 at 16:49
Thanks for the suggestion. –  Max Oct 4 '12 at 16:54
I agree with Qiaochu. If $f$ eventually dominates $g$, that means that expressions of the form $f(x) + g(x)$ behave like $f(x)$ when $x$ is sufficiently large. The canonical example is that the leading term of a polynomial dominates the others. That's not what you say that you want to say here. –  MJD Oct 5 '12 at 2:41