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*To*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] a minus times a plus*From*: Steve Gabosch <stevegabosch@me.com>*Date*: Mon, 27 Apr 2009 19:19:28 -0700*Delivered-to*: xmca@weber.ucsd.edu*Domainkey-signature*: a=rsa-sha1; s=2007001; d=ucsd.edu; c=simple; q=dns; b=MMpMkRCHKcKCJm3DtwOjInPbRUyfypH+tyi237CnqupjrhO/PpQfgttm6R21PJKlZ Hc97UKoblPUBE2uJaFA/g==*In-reply-to*: <0193A85F-03A7-4811-B912-217722A5770B@uvic.ca>*List-archive*: <http://dss.ucsd.edu/mailman/private/xmca>*List-help*: <mailto:xmca-request@weber.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>*List-post*: <mailto:xmca@weber.ucsd.edu>*List-subscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=subscribe>*List-unsubscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=unsubscribe>*References*: <30364f990904271547o5b4df21eifca69bf8318483f2@mail.gmail.com> <2C46D7A7-AD94-441C-AABD-269045835E3D@umich.edu> <0193A85F-03A7-4811-B912-217722A5770B@uvic.ca>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu

Luckily, I didn't have to try to explain to him why -8 * -8 = 64. - Steve On Apr 27, 2009, at 5:34 PM, Wolff-Michael Roth wrote:

Can't you think like this---perhaps it is too much of a physicist'sthinking. We can think of the following general function (operatorin physics) that produces an image y of x operated upon by A.y = Axif x is from the domain of positive integers, then A = -1 wouldproduce an image that is opposite to the one when A = +1, theidentity operation.Conceptually you would then not think in terms of a positive times anegative number, but in terms of a positive number that is projectedopposite of the origin on a number line, and, if the number isunequal to 1, like -2, then it is also stretched.The - would then not be interpreted in the same way as the + Cheers, Michael On 27-Apr-09, at 4:16 PM, Ed Wall wrote: MikeIt is simply (of course, it isn't simple by the way) because,the negative integers (and, if you wish, zero) were added to thenatural numbers in a way that preserves (in a sense) their (thenatural numbers) usual arithmetical regularities. It would beunfortunate if something that was true in the natural numbers was nolonger true in the integers, which is a extension that includesthem. Perhaps the easiest way to the negative x positive businessis as follows (and, of course, this can be made opaquely precise -smile):3 x 1 = 3 2 x 1 = 2 1 x 1 = 1 0 x 1 = 0so what, given regularity in the naturals + zero) do you thinkhappens next? This thinking works for, of course, for negative timesnegative. The opaque proof is more or less as follows.Negative numbers are solutions to natural number equations of theform (I'm simplifying all this a little)x + a = 0 ('a' a natural number)and likewise positive numbers are solutions to natural numberequations of the formy = b ('b' a natural number)Multiplying these two equations in the usual fashion within thenatural numbers givesxy + ay = 0 or substituting for y xy + ab = 0 so, by definition, xy is a negative number.Notice how all this hinges on the structure of the natural numbers(which I've somewhat assumed in all this).Ed On Apr 27, 2009, at 6:47 PM, Mike Cole wrote:Since we have some mathematically literate folks on xmca, couldsomeoneplease post an explanation of why multiplying a negative number by a positive numbers yields a negative number? What I would really love is an explanationthat is representable in a manner understandable to old collegeprofessorsand young high school students alike. mike _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca_______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca

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**Follow-Ups**:**Re: [xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**References**:**[xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**Re: [xmca] a minus times a plus***From:*Ed Wall <ewall@umich.edu>

**Re: [xmca] a minus times a plus***From:*Wolff-Michael Roth <mroth@uvic.ca>

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