So formally we say that a function T of N is little O of F of N, if and only if for all constants C, there is a constant N naught beyond which T of N is upper bounded by this constant multiple C times by F of N. So the difference between this definition and that of Big-O notation, is that, to prove that one function is big O of another, we only have to exhibit one measly constant C, such that C times F of N is upper bound, eventually, for T of N. By contrast, to prove that something is little O of another function, we have to prove something quite a bit stronger. 