# iteration

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:

 $f^{0}(x)=x$

and

 $f^{n+1}(x)=f(f^{n}(x))$

for nonnegative integers $n$. If $f$ is invertible, then by going backwards we can define the iterate also for negative $n$.

Title iteration Iteration 2013-03-22 12:43:40 2013-03-22 12:43:40 mathwizard (128) mathwizard (128) 9 mathwizard (128) Definition msc 26A18 iterate