# User:IssaRice/Computability and logic/Diagonalization out of a class

From Machinelearning

**Diagonalization out of a class** is a trick used to define a function that is not in a given list of functions.

Let be some class of total functions. If we are given an enumeration of such as then we can define a new total function . Now given any , we have . Thus, for every , so .