Good points about the cross product, but :
> We used to think as negative numbers being a generalization of the integers
"used to" ?
> We don't call them "real" numbers outside of math circles anymore.
Sure we do ?
> We used to think as negative numbers being a generalization of the integers
"used to" ?
> We don't call them "real" numbers outside of math circles anymore.
Sure we do ?
To clarify, we used to think of integers as just the natural numbers. Integer was a colloquial word meaning "whole, entire", so there was presumably a discussion about how negative numbers were whole or entire, though I vaguely remember this historical story. My point is just that at some point negative numbers were seen as a advanced extension of the natural numbers. Even zero was seen as an unnatural extension, which is why there is a confusion to this date as to whether "natural" numbers include zero.
ref: http://mathforum.org/library/drmath/view/57212.html
Not the best reference, but I've read it elsewhere, so maybe it's a myth, but someone can trace it to the source if they want.
> We don't call them "real" numbers outside of math circles anymore.
I mean laypeople don't know what the real numbers are in distinction to the rationals, for example.
Then again, with these conversations, the N < Z < Q < R < C... classification automatically pops in your mind if you did mathematics in last classes of high school (that's going to be a LOT of laypeople ! Of course, a lot of them, those that rarely encounter them, might then forget about this classification.)
And integers are still called "natural integers", and negative numbers are NOT called "natural" ?