WebMath: standard notation for negative numbers?

[Robert Miner]

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

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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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