In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average".
Let f be an arithmetic function. We say that an average order of f is g if
as x tends to infinity.
It is conventional to choose an approximating function g that is continuous and monotone. But even thus an average order is of course not unique.
Read more about Average Order Of An Arithmetic Function: Examples, Better Average Order, See Also
Famous quotes containing the words average, order, arithmetic and/or function:
“... to be successful a person must attempt but one reform. By urging two, both are injured, as the average mind can grasp and assimilate but one idea at a time.”
—Susan B. Anthony (1820–1906)
“There is a quality even meaner than outright ugliness or disorder, and this meaner quality is the dishonest mask of pretended order, achieved by ignoring or suppressing the real order that is struggling to exist and to be served.”
—Jane Jacobs (b. 1916)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“Nobody seriously questions the principle that it is the function of mass culture to maintain public morale, and certainly nobody in the mass audience objects to having his morale maintained.”
—Robert Warshow (1917–1955)