Re: Why should -1 multiplied by -1 be plus 1 and not -1

From: G. Frege (no_spam_at_aol.com)
Date: 08/06/04 

Date: Fri, 06 Aug 2004 12:15:58 +0200

On Fri, 6 Aug 2004 09:43:39 +0000 (UTC), ">parr\(*>"
<gniKyruaL@tenretnitb.moc> wrote:

>
> As a matter of interest, did you genuinely think that introducing
> the distributive law would help fix someone's wrong intuition?
>
Depends. "Intuition" is a vague term: there is a "intuition" which grows
with mathematical knowledge!

Btw, did you see my simplified try?

<Begin copy>
---------------------------------------------------------

Gina asked:

        "Why should -1 multiplied by -1 be plus 1 and not -1"

Well, at least I could make a case why -1 * -1 is NOT -1. (And if the
ONLY alternative for Gina is between -1 and 1 this would explain why
-1 * -1 has to be 1.)

Assume this w e r e the case:

        -1 * -1 = -1,

then we could just divide both sides by -1, and we would get:

        -1 = -1/-1.

Now a/a is certainly 1 for ANY number a (other than 0).

Hence we w o u l d get:

        -1 = 1.

But that's certainly n o t the case. Hence our assumption was false.
Hence

        -1 * -1 =/= -1.

Probably that helps to accept the infamous

        -1 * -1 = 1.

:-)

-----------------------------------------------------
<End of copy>

F.

P.S.
We make use of the following proof principle:

        A -> B -> C -> ... -> D
                  ~D
        -----------------------
                  ~A

In words: If we have shown that some assumption A implies B, which
implies C which ... which finally implies D. But we have n o t D, then
we also must have n o t A. (Since if we h a d A we also would have D,
but actually we have n o t D. Hence A c a n't hold.)

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