Definition:Ordering on Natural Numbers/Peano Structure
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Definition
Let $\struct {P, 0, s}$ be a Peano structure.
The ordering of $P$ is the relation $\le$ defined by:
- $\forall m, n \in P: m \le n \iff \exists p \in P: m + p = n$
where $+$ denotes addition in $\struct {P, 0, s}$.
Sources
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 4$: Number systems $\text{I}$: Peano's Axioms