We have to prove that, for every single constant C, no matter how small, for every C, there exists some large enough N naught beyond which T of N is bounded above by C times F of N. So, for those of you looking for a little more facility with little O notation, I'll leave it as an exercise to prove that, as you'd expect for all polynomial powers K, in fact, N to the K minus one is little O of N to the K. There is an analogous notion of little omega notation expressing that one function grows strictly quicker than another. 