===== Arithmetic structure of natural numbers =====
==== Set ====
| @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb N,+,\cdot \rangle$ |
| $ m=S(k) $ |
| @#55EE55: postulate   | @#55EE55: $n + 0 = n$ |
| @#55EE55: postulate   | @#55EE55: $n + m = S(n) + k$ |
| @#55EE55: postulate   | @#55EE55: $n \cdot 0 = 0$ |
| @#55EE55: postulate   | @#55EE55: $n \cdot m = n + (n \cdot k) $ |

==== Discussion ====
>todo: rewrite the defintion in my current notation

We'll often omit the multiplication sign.
=== Reference ===
[[http://en.wikipedia.org/wiki/Peano_axioms|Peano axioms]]
==== Parents ====
=== Context ===
[[Successor set]]
=== Requirements ===
[[Natural number]]
=== Element of ===
[[Commutative semiring]]
=== Related ===
[[Cardinal arithmetic with types]]