>nonnegative integers, Why, prey tell, did you make a distinction between positive and negative integers? Is it that repeated addition starts to fail as concep

>nonnegative integers, Why, prey tell, did you make a distinction between positive and negative integers? Is it that repeated addition starts to fail as conceptual model there? >the fact that my multiplication is equivalent to repeated addition for nonnegative integers, .. Your claim seems to be that in some abstract way any algorithmic approach to multiplication relies on the fact that multiplying non-negative integers (there's that distinction again .. nasty stuff those negative integers are for your argument) can be rewritten as a repeated addition ... but that's not how people (not even children learning multiplication) do it. That's not how computers do it either. So no, algorithmically multiplying numbers is not the same thing as 'using' the concept of 'multiplication is repeated addition' in any sense, colloquial or otherwise. Also it starts feeling like you're begging the question when you claim that.