Iota function

The iota function is a googological thought experiment proposed by Lawrence Hollom.

Define the iota function set as the set of all functions ever described. For simplicity, we shall restrict these functions:


 * \(f: \mathbb{N}^+ \mapsto \mathbb{N}^+\).
 * \(\forall n: f(n) \geq n\)
 * \(f\) is not the iota function.

Then \(I(n)\) is the largest possible value of \(F(n)\), where \(F\) is formed by composing all the functions in the iota function set in any order.