[peterwoerner]

But you can define multiplication based on abstracting repeated addition. That how we did it my analysis class, although I forget some of the details. So if you say multiplication is repeated addition, it really isn't a lie.

[threatofrain]

But did your analysis class define addition on the naturals? Then that's an operator for the naturals. And then for integers, rationals, etc.

[peterwoerner]

Yep and how to construct, the naturals from set theory, the integers from the naturals, the rationals from the integers and the reals from the rational. I've forgotten the details at this point, but I remember the conclusions.