User blog comment:Pellucidar12/My (probably futile) attempt at the largest number/@comment-1605058-20161029181347

I'm afraid the notion of "dominates ... to the same extent ..." is not well-defined. Certainly just a number of examples is not enough to make this precise, and we would need some sort of measure of by how much a function dominates another function, so that we can say c(n) dominates b(n) as much as b(n) dominates c(n). I can't think of a way to define that.