In article <firstname.lastname@example.org>, "Guillermo Phillips" <Guillermo.Phillips@marsman.demon.co.uk> wrote:
> Hello All, > > Here's something I've always wondered (perhaps in my naivety). Why > should -1 x -1 = 1? > I appreciate that lots of nice things come from this, but what's the > fundamental reason for it? >
Because 1 times anything is anything. That's the essential quality of one-ness, what mathematicians call a multiplicative identity. 1 does the same thing for multiplication that 0 does for addition, namely "leave the other thing unchanged."
If you have the concept of multiplication, then you have the concept of multiplying a number by a number, and then you must philosophically have the concept of NOT multiplying a number by a number. What is the result of NOT multiplying 5 by anything? 5, right? So "multiply by 1" is a synonym for "don't multiply at all."