Definition
The formal definition of an iterated function on a set X follows.
Let X be a set and f: X → X be a function.
Define f n as the n-th iterate of f, where n is a non-negative integer, by:
and
where idX is the identity function on X and denotes function composition; that is, .
Because the notation f n may refer to both iteration (composition) of the function f and exponentiation of the function f, some mathematicians choose to write f °n for the n-th iterate of the function f.
Read more about this topic: Iterated Function
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)