> And, you drop the least significant terms of f(x) because g(x) dominates them, i.e. lim_{x -> \infty} g(x)/f(x) = 0. If g(x) dominates all the terms in f(x),

> And, you drop the least significant terms of f(x) because g(x) dominates them, i.e. lim_{x -> \infty} g(x)/f(x) = 0. If g(x) dominates all the terms in f(x), then wouldn't lim_{x -> \infty} g(x)/f(x) go to infinity?