## 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.