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Re: Multiple Multiplication Mea
Posted:
Jul 31, 1997 5:10 PM


Prof Boulet wrote: ************************* How can minus have two senses and plus not? The unary operator of minus in negative numbers could not be defined if not relative to another unary operator for the positives!!! ************************* Well, we seem to be getting off into excessive gory detail. The minus sign () is used in any RING in two different but closely allied ways: 1. for any element b, we denote its additive inverse by b ; but 2. we also write c  b as an abbreviation for c + (b) and this is the operation of subtraction. The plus sign (+) is used in only one way as the sign for the operation of addition. That is generic stuff. 3. But in the integers, rationals and real numbers, we have the additional property of having a compatible order relation and we use the standard HinduArabic decimal system for naming our POSITIVE numbers and zero. Then for negative numbers we simply put a  in front of the name (symbol) for a positive number to denote the negative number. It is of course the additive inverse of the positive number, and it is the only real name we have for that negative number. Does that not seem to be another use of  , as part of our standard name of the neg. number?
Ladnor Geissinger Math Prof at UNC Chapel Hill & Math Chair at IAT email: ladnor.iat@mhs.unc.edu or ladnor_geissinger@unc.edu phone: 9194051925 address: Institute for Academic Technology 2525 Meridian Parkway, Suite 400 Durham NC 27713 USA IAT phone: 9195605031 IAT fax: 9195605047 IAT web home page: www.iat.unc.edu LEARN NC home page: www.learnnc.org Mathwright Library: ike.engr.washington.edu/mathwright/



