Definition:Successor Mapping on Natural Numbers

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

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


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

From Peano's Axioms Uniquely Define Natural Numbers, this is seen to be an instance of a successor mapping.