Every function maps each entity in some domain onto exactly one entity in some range. But while every function thus determines a set of ordered pairs, Frege (1891) did not identify functions with such sets. He said that a function “by itself must be called incomplete, in need of supplementation, or unsaturated. And in this respect functions differ fundamentally from numbers (p. 133).” For example, we can represent the successor function as follows, with the natural numbers as the relevant domain