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:
“When we dream about those who are long since forgotten or dead, it is a sign that we have undergone a radical transformation and that the ground on which we live has been completely dug up: then the dead rise up, and our antiquity becomes modernity.”
—Friedrich Nietzsche (1844–1900)