An additive function f(n) is said to be completely additive if f(ab) = f(a) + f(b) holds for all positive integers a and b, even when they are not co-prime. Totally additive is also used in this sense by analogy with totally multiplicative functions. If f is a completely additive function then f(1) = 0.
Every completely additive function is additive, but not vice versa.
Read more about this topic: Additive Function
Famous quotes containing the word completely:
“That the world is not the embodiment of an eternal rationality can be conclusively proved by the fact that the piece of the world that we know—I mean our human reason—is not so very rational. And if it is not eternally and completely wise and rational, then the rest of the world will not be either; here the conclusion a minori ad majus, a parte ad totum applies, and does so with decisive force.”
—Friedrich Nietzsche (1844–1900)