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Re: Multiple Multiplication Mea
Posted:
Jul 31, 1997 12:54 PM
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Prof Boulet wrote in response to my earlier note:
***********************************************************
Even my calculator has both the binary +/- and the unary +/-!
If "plus" and "minus" only refer to addition and subtraction, what sense
can
you make of "3 - - 4", i.e. what does "subtract subtract" mean?
At 05:01 PM 7/30/97 -0500, you wrote:
>A recent note to amte had a statement that caught my eye:
><<<<<<<<<<<<<<<<<<<
> However, if you
>take "plus" and "minus", there you start running into ambiguities.
>"Plus"
>can be a binary operator of addition, or it can be a unary operator of
>direction in the case of defining the integers.
>>>>>>>>>>>>>>>>>>>
>Let's not go overboard. Plus (+) refers only to the operation of
>addition, there is no unary operator of positive direction. Just look
at
>your calculator. There is no + put in front of positive numbers (it
>would be redundant), the button that has + on it is for addition and
that
>alone. There is a button with plus/minus
>which is used to change the sign of the number in the display (i.e. 3
>goes to -3, or -7 goes to 7). It is enough of a problem that minus (-)
>is used in two quite different senses -- don't compound this by
>unnecessarily having two senses for +!
********************************************************
The question of course is about whether the plus sign is used "in
mathematics" in two quite different senses. My earlier note said no it
isn't, but that of course the minus sign is. The point about the
calculator is that, as elsewhere in maths, we do not use + in front of 3
to indicate that 3 is positive, so that mathematically the only use for +
is for the binary operation of addition between two expressions. On the
other hand, "on the calculator" there is an occasional need to change the
sign of a number that is currently on the input/output display. Thus an
extra button has been provided for this editing function, and it usually
has the short conventional symbol "+/-" on it instead of something longer
like "sign" or "reverse" or ....
Makers of inexpensive calculators assume that if a user presses two
binary operation buttons consecutively then the first must have been a
mistake, and so the calculator automatically deletes the first and keeps
only the second. So if you key in the string 5 - - 3 it retains it
internally as 5 - 3 but you just see 3 on the display [until you press
any operation button and it evaluates whats there already and displays it
-- on most calculators], whereas if you key in the string 5 - 3 +/- it
retains it internally as 5 - (-3) and displays -3.
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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