iteration

Let $f:X\to X$ 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 $n$.