Date: Sep 19, 1999 12:01 AM
Author: carel
Subject: Re: -1 x -1 ?

John Savard wrote in message <37e3ccff.1687863@news.prosurfr.com>...

>"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".

>

>John Savard ( teneerf<- )

>http://www.ecn.ab.ca/~jsavard/crypto.htm

Or how about the following

-1 x 0 = 0

-1 x (1-1) = 0

(-1 x 1) + (-1 x -1 ) = 0

-1 + (-1 x -1) = 0

-1 + 1 + (-1 x -1) = 1

0 + (-1 x -1 ) = 1

-1 x -1 = 1

Carel