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iteration (Definition)

Let $ f\colon X\to X$ be a function, $ X$ being any set. The $ n$-th iteration of a function is the function which is obtained if $ f$ is applied $ n$ times, and is denoted by $ f^n$. More formally we define:

$\displaystyle f^0(x)=x$
and
$\displaystyle f^{n+1}(x)=f(f^n(x))$
for nonnegative integers $ n$. If $ f$ is invertible, then by going backwards we can define the iterate also for negative $ n$.



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Other names:  iterate
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Cross-references: negative, invertible, integers, function
There are 54 references to this entry.

This is version 6 of iteration, born on 2002-06-04, modified 2003-06-15.
Object id is 3027, canonical name is Iteration.
Accessed 7782 times total.

Classification:
AMS MSC: 26A18 (Real functions :: Functions of one variable :: Iteration)
Pending Errata and Addenda
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