## Arithmetic structure of natural numbers

### Set

 definiendum $\langle \mathbb N,+,\cdot \rangle$ $m=S(k)$ postulate $n + 0 = n$ postulate $n + m = S(n) + k$ postulate $n \cdot 0 = 0$ postulate $n \cdot m = n + (n \cdot k)$

### Discussion

todo: rewrite the defintion in my current notation

We'll often omit the multiplication sign.