Definition:Peano Structure

Definition
A Peano structure $\mathcal P = \left({P, 0, s}\right)$ is a set $P$ together with:


 * A mapping $\exists s: P \to P$ which is:
 * injective
 * specifically not surjective.


 * An element (usually denoted $0$ or a variant) such that $0 \in P \setminus s \left({P}\right)$, where:
 * $\setminus$ denotes set difference;
 * $s \left({P}\right)$ denotes the image of the mapping $s$.

Also known as
A Peano structure is also known as a Dedekind-Peano structure.

Also see

 * Peano Structure satisfies Peano Axioms


 * Non-Successor Element of Peano Axiom Schema is Unique, which justifies the singling out $0$ as a specifically distinguished element of $P$.

They were formulated by Peano, and were later refined by Dedekind.