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:

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

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

Sources

• 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): $\S 2.4$: Example $1$
• 1982: Alan G. Hamilton: Numbers, Sets and Axioms ... (previous) ... (next): $\S 1$: Numbers: $1.1$ Natural Numbers and Integers: Examples $1.1 \ \text {(c)}$