Date: Sep 20, 1999 6:37 PM
Author: Jonathan Hoyle
Subject: Re: -1 x -1 ?



> Here's something I've always wondered (perhaps in my naivety). Why
> should -1 x -1 = 1?


Consider the following situation. Suppose you had a prison which costs
the tax payers $1000 per inmate per day in taxes. Thus the daily
"revenue" to the community is -$1000. Now, let's say one of those
inmates escaped. The total change in revenue is:

-1 prisoner X -$1000 per day = +$1000 per day.


Something more mathematically concrete:

1. 0 X -1 = 0 // 0 times anything (finite) is 0
2. (1-1) X -1 = 0 // substitute 0 for 1-1
3. (1 + -1) X -1 = 0 // subtracting = adding a negative
4. (1 X -1) + (-1 X -1) = 0 // distribution of mult. over add.
5. -1 + (-1 X -1) = 0 // 1 X anything is that anything
6. 1 + -1 + (-1 X -1) = 1 + 0 // Add 1 to both sides
7. -1 X -1 = 1 // Q.E.D.

Someone could probably demonstrate this in less than 7 steps, but this
will. In any case, one of the above mathematical steps must become
invalid (DMA, multiplicative identity, etc.) if -1 X -1 were not 1.