"Guillermo Phillips" <Guillermo.Phillips@marsman.demon.co.uk> wrote, in part:
>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?
Well, negative numbers are kind of strange, almost like imaginary numbers. You have an empty box, and you can leave it empty, or you can put one pebble in it, or you can put two pebbles in it, and so on.
But negative numbers can make sense for things like temperature and bank accounts.
If you owe five dollars, that can be considered a way of having -5 dollars.
If you owe three people five dollars, you have 3 * -5 dollars, or -15 dollars.
If three people owe you five dollars, then you have an asset that is (hopefully, if they're honest) worth 15 dollars. So that's -3 * -5, the minus on the 3 standing for the fact that the debt is "the other way around".