Iteration

Iteration is a fundamental concept in googology in which a function is composed with itself repeatedly.http://www.geometer.org/mathcircles/iterated.pdf Given a function \(f \colon X \to Y\) with \(X \supseteq Y\), we use \(f^n(x)\) to refer to the result when applying \(f\) to \(x\) \(n\) times. Formally, \(f^0(x) = x\) and \(f^{n + 1}(x) = f(f^{n}(x))\).
== Examples ==
* Graham's number can be defined as \(G^{64}(4)\) where \(G(n) = 3\uparrow^{n}3\).
* Fast-growing hierarchy includes definition of \(f_{\alpha+1}(n) = f^n_\alpha(n)\)
== Sources ==
Category:Concepts