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Math Forum » Discussions » sci.math.* » sci.math.independent

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

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Henry

Posts: 1,089
Registered: 12/6/04
Re: -1 x -1 ?
Posted: Jan 22, 2009 3:54 AM
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On 22 Jan, 01:51, Tay <wintct...@gmail.com> wrote:
> -1 *-1 = 1 huh?
> The minus (negative) signs cancel eachother out:
> (-1)(-1) = [(-)(-)](1x1) = (+)(1x1) = +1
> It's so simple.

How do you know the two negative signs cancel each other out in
multiplication?

With (-x) being the additive inverse of x in a [unitary] ring,
I would allow you (-(-x)) = x, i.e. (-x)+x = 0 and x+(-x) = 0.
You can also have 1*x = x, x*1 = x, x*0 = 0 and 0*x = 0.

Consider (-1)*1 + (-1)*(-1) = (-1) * (1+(-1)) = (-1) * 0 = 0.
But (-1)*1 = (-1).
So (-1) + (-1)*(-1) = 0 and so (-1)*(-1) = 1.

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