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.