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:
“You will find the most pronounced hatred of other nations on the lowest cultural levels. There is, though, a level where the hatred disappears completely and where one so to speak stands above the nations and where one experiences fortune or misfortune of a neighboring country as if they had happened to one’s own.”
—Johann Wolfgang Von Goethe (1749–1832)