Definition:Successor Mapping on Natural Numbers

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Let $\N$ be the set of natural numbers.

Let $s: \N \to \N$ be the mapping defined as:

$s = \left\{{\left({x, y}\right): x \in \N, y = x + 1}\right\}$

Considering $\N$ defined as a Peano structure, this is seen to be an instance of a successor mapping.