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At 00:51 +0200 2001/05/21, Lars Hellström wrote:
>In what way does e.g.
>
>   Euclid was a geometer.
>
>contain more logical mark-up than
>
>   a \in A

I think that the markup that is in TeX, like $\in$, is not viewed by
mathematicians as logical markup, but merely a way to provide the glyphs
and a name that is easy to remember. The tie to "set membership" or
whatever mathematical quantity is weak, and if a mathematician would prefer
another glyphs than what TeX or LaTeX suggest, one would use that one

In fact, when the AMS-fonts were developed, one added some new glyphs in
order to cover up for this practise: One can note that there is a
\varnothing as an alternative to the TeX \emptyset, and two variations
\hbar, \hslash, as two variations for the Heisenberg constant.

I would prefer \varnothing to denote the empty set; and if I use that, it
looks to me as though as \emptyset could be used to denote something else.
As for the \hbar and \hslash, if it is a paper in physics, I would probably
avoid using them both side by side, because I think that a physicist might
confuse them. But a mathematician may not have the same problem.

So the best one could hope for, I think, is to build a layer above those
glyphs, say an empty set command that can expand to \emptyset or
\varnothing, a set membership command that can expand to either of \in or
the two epsilon variations, but there can be no restrictions on the glyphs
themselves in the sense that the use of one of them prohibits the other.

Hans Aberg