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:
“After, when they disentwine
You from me and yours from mine,
Neither can be certain who
Was that I whose mine was you.
To the act again they go
More completely not to know.”
—Robert Graves (1895–1985)