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Topic: -1 x -1 ?
Replies: 29   Last Post: May 13, 2009 9:01 AM

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 Jonathan Hoyle Posts: 398 Registered: 12/10/04
Re: -1 x -1 ?
Posted: Sep 20, 1999 6:37 PM

> 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.

Date Subject Author
9/16/99 Guillermo Phillips
9/16/99 Ian A. Mason
9/16/99 Peter Percival
9/16/99 Dave Seaman
9/17/99 Steve Leibel
9/17/99 Dale Henderson
9/18/99 Peter Percival
9/18/99 Bill Taylor
9/18/99 John Savard
9/19/99 carel
9/20/99 Jon Haugsand
9/20/99 HH
9/20/99 Jon Haugsand
9/20/99 Jonathan Hoyle
9/20/99 Jim Hunter
1/21/09 Tay
1/21/09 mensanator
1/21/09 lwalke3@lausd.net
1/22/09 Henry
1/22/09 David R Tribble
1/22/09 Dave L. Renfro
1/22/09 mensanator
5/12/09 Kayama
5/12/09 mensanator
5/12/09 hagman
5/12/09 Bill Dubuque
5/12/09 Bill Taylor
5/13/09 Cobra
5/13/09 Cobra