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.
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Famous quotes containing the word completely:
“Physically there is nothing to distinguish human society from the farm-yard except that children are more troublesome and costly than chickens and calves and that men and women are not so completely enslaved as farm stock.”
—George Bernard Shaw (1856–1950)