WebMath: standard notation for negative numbers?

[June Lester]

>Date: Mon, 22 Jul 2002 10:13:09 -0500
>Message-Id: <200207221513.KAA29124 at wisdom.geomtech.com>
>From: Robert Miner <RobertM at dessci.com>
>To: webmath at camel.math.ca
>CC: webmath at camel.math.ca
>Subject: Re: WebMath: standard notation for negative numbers?
>
>
>Hi.
>
>> Is there an international standard in notation for negative numbers?  One
>> enquirer has asked:
>>
>> "Personally, I have been brought up differentiating between 'negative
>>seven'
>> and 'subtract seven' through the former being a 'raised' sign compared
>>with the
>> subtraction sign.  However, is this 'standard' world-wide or is there no
>>agreed
>> standard?  I note on several web sites that often a raised sign is not
>>used for
>> 'negative' and a 'subtraction' sign is used instead.  However, I don't know
>> whether that is because that is standard in that country or whether they
>>are
>> just being 'lazy' (also, of course, the issue of computers may make
>>people not
>> bother using a raised sign as it is not as easy to produce on a computer
>>as a
>> standard subtraction sign).  Of course, it may well be the case that
>>there is
>> no standard at all."
>
>My take on this is that the "raised" minus sign is mostly a
>pedagogical convention.  I thrives in the world of handwritten
>mathematics, but is rare in typeset mathematics.
>
>In Unicode 3.2 (which is the newest version which include several
>thousand new characters for math) there are a couple relevant
>charaters:
>
>0x002d (45)	HYPHEN-MINUS
>0x2122 (8482)   MINUS SIGN
>
>Typically in fonts, the hyphen minus (which is the one on the
>keyboard) is shorter, thicker, and sometimes a little raised.  The
>true minus is the longer, thinner more TeX-like symbol.
>
>In a web page where you are faking the math, you are probably stuck
>using hyphen minus.  But in most math typesetting software, including
>the main MathML implementations, usually a hyphen minus in math markup
>is interpreted as being the true minus as a convenience.  Obviously
>that works against using the hyphen minus as a stand in for the
>"raised minus", but since that doesn't work dependably anyway that's
>probably not a bad thing.
>
>To get a dependable, clearly different raised minus, I would use a
>regular minus as a superscript to an space or something like that.
>
>My own view of the standard way of distinguishing the
>unary minus from the binary minus operator is that this is done with
>spacing, at least in typeset math.  A unary minus operator (the kind
>that you get with negative numbers) is sucked up close to its operand
>on the right, while the binary minus has fairly generous spacing on
>both sides: -2 vs 2 - 3.  When there's ambiguity, I think most typeset
>texts would use parens 2 - (-3), etc.
>
>--Robert
>
>------------------------------------------------------------------
>Robert Miner                                    RobertM at dessci.com
>MathML 2.0 Specification Co-editor                    651-223-2883
>Design Science, Inc.   "How Science Communicates"   www.dessci.com
>------------------------------------------------------------------
>
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