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Re: Binary Relations, draft 1

At 20:38 +0000 1998/11/17, Chris Rowley wrote:
>> If you look at reasonable quality math text, then names such as "sin",
>> "cos" are almost invariably typeset upright and expressions like f(x) are
>> typeset in italics. Even simple WYSIWYG math processors seems to know the
>> difference.
>Yes indeed but, according to the folklore i heard at my professor's
>knee, this has nothing to do with contsants/variables (whatever
>they are???).

One way to extrapolate a general rule form the empiricism in use is the
rule I gave, and different people seem to arrive at the same or similar

It is not possible to say that this is so or not, because the traditional
usage is wholly empirical.

The traditional typographical explanation, or rule, that names such as
"sin", "cos" should be typeset upright is that these are functions. But
this does not explain why the "f" in f(x) should be typeset as a variable,
when it clearly is a function. One also needs to change the rule so that it
becomes useful in modern mathematics, which does not circulate around
functions in the same way it did the last century.

So the underlying principle seems to be that names that have one consider
to have a fixed meaning should be typeset upright, and the others should be
typeset slanted/italics.

Then it is of course so that no mathematician will ever accept a rule of
any kind be imposed like that, as each paper is dictated by the condition
to bring out the notions, where the notation is just a tool. With TeX, the
situation is different than in the past, because every mathematician can
make their own choice, and it is probably best for the publisher not to
meddle with these things.

But if one wants to have a general rule, this is one might use.

  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/>