Pairing function

In mathematics a pairing function is a process to uniquely encode two natural numbers into a single natural number.

Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers. In theoretical computer science they are used to encode a function defined on a vector of natural numbers ${\displaystyle f:\mathbb {N} ^{k}\rightarrow \mathbb {N} }$ into a new function ${\displaystyle g:\mathbb {N} \rightarrow \mathbb {N} }$.

A pairing function is a primitive recursive bijection

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