function f is not determined merely by specifying its domain X, and the function values f(x) for each point in that domain x ∈ X. Rather, one must also specify what is called the codomain of the function, the space Y of intended target values for the function f: X → Y. The codomain is not the same as the range of the function, because not every y ∈ Y needs to be realized as a value f(x).
