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Re: Binary Relations, draft 1

At 00:55 +0000 1998/11/18, Chris Rowley wrote:
>> 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
>> rule.
>But an empicist approach, and Occam's razor, I think would then
>suggest to you that Bethold's extrapolation (which is not entirely
>empirical) is superior.

Sorry, I do not know about Bethold's extrapolation -- so you will have to
explain what you mean.

>> 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.
>No rules, please (at least not generated in this forum).

Let's restating the main rule for typesetting pure mathematics:
    There is no typesetting rule of pure math.

>> But if one wants to have a general rule, this is one might use.
>One rule is a s good as another to a drowning ISO committee but, as
>you suggest, not useful for mathematics.

It is of course not happy that the ISO committee charges away with its own
typesetting definitions, because what may happen is that journals may be
enforcing them in the belief that these ISO standards have a wider
applicability than they actually do, giving some serious headache to the

As for Unicode, Unicode does not tell people how to use the symbols; it
merely provides them.

So with respect to Unicode, the discussion about these rules is this: Are
these different font shapes merely different styles that can be provided by
the typesetter, or is it semantic differences that to the mathematician
makes the different shapes to in effect be different symbols to the

If it is the former case, then according to the Unicode rules, the
different shapes should not be provided, but if it is the latter case, then
they should be provided.

Now, I think that it is definitely the latter case: For example, it is more
and more becoming a standard that BlackBoard R denotes the set of reals;
then, in effect, this has become a new symbol which is hard to dispense
with for the mathematicians using it.

So I think those different shapes should definitely be provided: This
allows them to naturally develop into more fixed conventions about how they
should be used. I think also such a development will happen when different
fields start to interact more with each other.

  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/>