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
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