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Re: Multiple Multiplication Mea
Posted:
Jul 31, 1997 5:10 PM
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Prof Boulet wrote:
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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!!!
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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 Hindu-Arabic 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: 919-405-1925
address: Institute for Academic Technology
2525 Meridian Parkway, Suite 400
Durham NC 27713 USA
IAT phone: 919-560-5031
IAT fax: 919-560-5047
IAT web home page: www.iat.unc.edu
LEARN NC home page: www.learnnc.org
Mathwright Library: ike.engr.washington.edu/mathwright/
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