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:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)