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 $n$