Definition:Successor Mapping

Definition
Let $\left({P, s, 0}\right)$ be a Peano structure.

Then the mapping $s: P \to P$ is called the successor mapping on $P$.

The image element $s \left({x}\right)$ of an element $x$ is called the successor element or just successor of $x$.

Also known as
The successor mapping can also be seen referred to as the successor function.