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Re: empty set symbol in MathML

From: David Carlisle <davidc@nag.co.uk>
Date: Mon, 5 Apr 2004 23:42:04 +0100
Message-Id: <200404052242.XAA24514@e3000>
To: Strotmann@rrz.uni-koeln.de
Cc: www-math@w3.org

Early MathML releases did distinguish these, but used the private use
area extensively, after Unicode 3.1 and 3.2 added most of the characters
MathML agreed to drop the use of the private use area so is constrained
to use official Unicode allocations.

As Andreas indicated, one reason why Unicode did not add a second empty
set symbol was that it would clash with a combination of 0 with a
combining / (They have a general policy of _not_ adding precomposed
variants of characters that may be constructed by composing characters,
except where those characters have already been added, either in unicode
or in some legacy encoding that's being incorporated into unicode.)

This reasoning would lead to the assignments
empty: 0030 0338 slashed 0
varnothing:  2205 slashed circle
which would be consistent from a Unicode and amsLatex viewpoint, but...

MathML also tries to be compatible with XHTML, as in an XHTML+MathML
document, the entity empty can only have one meaning, it can not mean
one thing in the html bits, and something else in mathml. HTML and XHTML
define empty to be 2205. Also support for combining characters in
existing renderers at the time these assignments were made was (perhaps
is) not always there, and it would seem dangerous to change an existing
assignment of empty from 2205 to use a combining combination that may or
may not display correctly in deployed systems.

So the situation is not ideal, but comes from trying to be compatible
with several incompatible formats...

In this case I think it really is just a glyph variant, the varnothing
character added to the TeX repertoire by the AMS fonts is more of a
correction for the dubious glyph used for the empty symbol in the
standard cm fonts, rather than a semantically different character.

Of course the issue comes up again now in the draft ISO standardisation
of these entities (see http://www.w3.org/2003/entities) which currently
follows MathML and makes empty and emptyv synonyms, but I suspect that
it should not do this...

Received on Monday, 5 April 2004 18:42:13 UTC

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