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Re: Math Arrows and Harpoons

At 09:05 -0500 1998/11/13, Barbara Beeton wrote:
>that's why i included the afii reference.  that is a standard glyph
>image, not just a suggestion.

All I am saying is that from what I know, the variation "leadsto" should
not have the arrowhead pointing upward. They may have another symbol, and
the fellow creating that standard should know its usage.

>i've also come upon the glyph (afii 042/070 = 2238) rightwavyarrow
>over dash (the dash is the same length as the arrow) with the glyph
>description "isomorphism mapping".

  In category theory, I think the normal thing is to either make the
isomorphism arrow both mono and epi >-->> in categories this implies an iso
(such as Abelian categories), or using a plain arrow  ---->  eith a \cong
symbol on the shaft.

> i don't know the source of this
>glyph, but the arrow definitely has the head pointing up to the right
>at very nearly a 46\degree angle.

  Of course, computer scientists and others use the words "monomorphism" in
other meanings than mathematicians. They may have invented their own
meaning and symbols. I have no idea why they want the arrow head pointing
upwards in such a case.

  There appears to be a problem with physicists and others being quick at
issuing standards, without first checking what mathematicians do: The
mathematics often requires more sophisticated tools than the applied
sciences do.

  As far as I am is concerned, if I can get the LaTeX \leadsto type arrows,
then I am satisfied.

>if a composite symbol is to be taken with a single meaning, then for
>unicode it requires a single code.

  The problem is that with the math symbols, there is ususally no single
meaning; it will vary from context to context. The idea of Unicode does not
work at all when trying to classify symbols for math use.

>in this case, not so, if i am to believe my contacts in the iso coding
>working group and the unicode technical committee.  unicode will not
>assign a code to something unless it has a clear meaning.  what they
>choose to call it in their published manual is something else again;
>that may well be descriptive of the shape rather than giving the actual
>meaning.

  So this is why ISO and Unicode will not be able to produce standards
which are suitable for mathematics in general, only much fitting a few more
specialized applied math areas. ISO and Unicode hold onto the wrong kind of
dogma simply:

  It is a mess: If the idea is "a character = a meaning", then the symbols
should be named like that, so that the original meaning can reconstructed.
The fact that they fail in the case of mathematics is because that the
dogma they work with is wrong from the outset.

  Hans Aberg
                  * Email: Hans Aberg <mailto:haberg@member.ams.org>
                  * Home Page: <http://www.matematik.su.se/~haberg/>
                  * AMS member listing: <http://www.ams.org/cml/>