Iteration

Iteration is a fundamental concept in classical googology in which a function is composed with itself repeatedly. Given a function \(f : X \mapsto Y\) with \(X \superseteq Y\), we use \(f^n(x)\) to refer to the result when applying \(f\) to \(x\) \(n\) times. Formally, \(f^0(x) = x\) and \(f^{n + 1}(x) = f(f^{n}(x))\).