Definition:Successor Mapping

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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 $x$.


Successor Mapping on Natural Numbers

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.


Also known as

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


Sources