Pi is definitely not a fractional number... I don't think it's cheating at all, multiplication on the naturals is repeated addition, that's not the case for the reals.
Sure it is, as long as you're willing to repeat in increments of real numbers.
And that's my point, basically - By the time we're discussing real numbers, we need multiplication as an operator, because we're discussing ratios already.
I wouldn't call the fact that pi is irrational an insight of "early mathematics." We knew that sqrt(2) was irrational around 500 BC if not earlier. We didn't know pi was irrational until around the time of the American revolution.
Interesting how computers (which only understand ‘1’ and ‘0’ can do multiplication of reals, then. Unless you’re intel, of course... (no, I will never let it go :)
Can we not consider that the algorithm taught for multiplication of real numbers is repeated multiplication of natural numbers which can be seen as repeated addition of natural numbers so we could define an addition only algorithm for multiplication of real numbers.
