# Codomain¶

In Maths^{1}, the codomain of a function is the set to which it's output belongs. The exact set of a functions output is known as its range.

## Backlinks¶

- A Programmers Introduction to Mathematics
- Topic: Maths
- Mathematical Functions
- A function in mathematics
^{1}is a relation between a value in a domain and a value in a codomain across a range. In programming terms, this means that mathematical functions are single-arity and pure. In other words, they take a single value and, given the same value, always produce the same output.

- A function in mathematics
- Range
- A pair of types with the same cardinality will always be isomorphic
- There will always be a way of exhaustively mapping each value of type a to type b, injectively and surjectively when viewing the domain and the codomain as a set.

- Language: Function over a set