The iota function is a googological thought experiment proposed by Lawrence Hollom.[1]

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

  • \(f\) maps positive integers to positive integers, and its outputs are greater than or equal to its inputs.
  • \(f\) is not the iota function or any similarly defined 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.

Clearly \(I(n)\) is not a well-defined function; it is intended to be a thought experiment and not a serious contender in the race for fast-growing functions. A "number" defined by the iota function is Hollom's number.

However, duplicate functions are not allowed


  1. Hollom, Lawrence. Iota function