Definition:Successor Mapping on Peano Structure/Successor Element

Definition

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

Let mapping $s: P \to P$ denote the successor mapping on $P$.

The image element $\map s x$ of an element $x$ is called the successor element or just successor of $x$.

Also see

• Results about the successor mapping can be found here.

Sources

• 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Introduction $\S 4$: The natural numbers
• 1964: J. Hunter: Number Theory ... (previous) ... (next): Chapter $\text {I}$: Number Systems and Algebraic Structures: $2$. The positive integers