Definition:Addition/Natural Numbers

Definition
Let $\N$ be the natural numbers.

Addition on $\N$ is the basic operation $+$ everyone is familiar with.

For example:


 * $2 + 3 = 5$
 * $47 + 191 = 238$

Every attempt to describe the natural numbers via suitaable axioms should reproduce the intuitive behaviour of $+$.

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