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.

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