Definition:Ordering on Natural Numbers

Definition
Let $\N$ denote the natural numbers.

The ordering on $\N$ is the relation $\le$ everyone is familiar with.

For example, we use it when we say:


 * James has six apples, which is more than Mary, who has four.

which can be symbolised as:


 * $6 \ge 4$

Every attempt to describe the natural numbers via suitable axioms should reproduce the intuitive behaviour of $\le$.

The same holds for any construction of $\N$ in an ambient theory.