Date: Sep 17, 1999 2:30 AM
Author: Steve Leibel
Subject: Re: -1 x -1 ?
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."
You asked a pretty deep question.