A completely multiplicative function (or totally multiplicative function) is an arithmetic function (that is, a function whose domain is the natural numbers), such that f(1) = 1 and f(ab) = f(a) f(b) holds for all positive integers a and b.
Without the requirement that f(1) = 1, one could still have f(1) = 0, but then f(a) = 0 for all positive integers a, so this is not a very strong restriction.
Read more about Completely Multiplicative Function: Examples, Properties
Famous quotes containing the words completely and/or function:
“The others “acted” a role; I was the role. She who was Mary Garden died that it might live. That was my genius ... and my sacrifice. It drained off so much of me that by comparison my private life was empty. I could not give myself completely twice.”
—Mary Garden (1874–1967)
“Any translation which intends to perform a transmitting function cannot transmit anything but information—hence, something inessential. This is the hallmark of bad translations.”
—Walter Benjamin (1892–1940)