| 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) $ |
todo: rewrite the defintion in my current notation
We'll often omit the multiplication sign.