Editing Pairing function (section)

==Definition==
A '''pairing function''' is a [[bijection]]
:<math>\pi:\mathbb{N} \times \mathbb{N} \to \mathbb{N}.</math>{{sfn|Pigeon}}{{sfn|Lisi|2007}}{{sfn|Regan|1992}}

===Generalization===
More generally, a pairing function on a set <math>A</math> is a function that maps each pair of elements from <math>A</math> into an element of <math>A</math>, such that any two pairs of elements of <math>A</math> are associated with different elements of <math>A</math>,{{sfn|Szudzik|2006}}{{efn|That is, an [[Injective function|injection]] from <math>A^2 \rightarrow A</math>.}} or a bijection from <math>A^2</math> to <math>A</math>.{{sfn|Szudzik|2017}}

Instead of abstracting from the domain, the arity of the pairing function can also be generalized: there exists an n-ary generalized Cantor pairing function on <math>\mathbb{N}</math>.{{sfn|Lisi|2007}}