# User:Dfeuer/Ordering on Natural Numbers/Peano

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## Definition

Let $\left({\N, 0, s}\right)$ be a Peano structure, where $\N$ is a set.

Let $<$ be the transitive closure of $s$.

Let $\le$ be the reflexive closure of $<$.

Then:

- $<$ is the
**usual strict ordering**of the natural numbers.

- $\le$ is the
**usual ordering**of the natural numbers.