Category:Definitions/Successor Mapping

This category contains definitions related to Successor Mapping.
Related results can be found in Category:Successor Mapping.

Let $V$ be a basic universe.

The successor mapping $s$ is the mapping on $V$ defined and denoted:

$\forall x \in V: \map s x := x \cup \set x$

where $x$ is a set in $V$.

Peano Structure

Let $\struct {P, s, 0}$ be a Peano structure.

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

Successor Mapping on Natural Numbers

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

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

$s = \set {\tuple {x, y}: x \in \N, y = x + 1}$

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