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At 12.19 +0200 2001-05-19, Hans Aberg wrote:
>At 17:29 +0200 2001/05/18, Lars Hellström wrote:
>>With TeX, the set membership relation symbol has _always_ been \in, not
>>\epsilon, but appearently you haven't used it enough to take that
>>distinction for granted. I'm not arguing that \in and \epsilon should be
>>identified (as they are clearly semantically distinct), I'm arguing that
>>\epsilon and \varepsilon (which are both greek letters called "epsilon"
>>when a formula is read aloud) should be identified in the internal LaTeX
>>representation of math characters.
>
>The reason one is getting stuck with it is for backwards compatibility, and

Indeed. \epsilon and \varepsilon could probably not be identified earlier
than in LaTeX3.

>further there is no guarantee that mathematicians will use the symbols the
>way you dictate.

You mean saying \in for the set membership relation rather than \epsilon?
\epsilon is just plain wrong (and has always been so) since it generates an
Ord math atom, not a Rel math atom as a relation command should.

>Later, one would expect LaTeX, or whatever scientific typesetting system,
>being capable to support them all without restrictions. Plus admitting

Yes, but not necessarily supporting them by default. There is an important
difference between the default set-up making \epsilon and \varepsilon
different, and providing a mechanism that makes it easy to (on a per
document basis) add such a distinction. What is provided by the default
set-up becomes the minimal core which _all_ set-ups must provide. The
larger you make this core, the bigger the effort needed to support it will
be, and the alternatives to the default will be correspondingly fewer. It's
easy to request that all fonts provide everything that is in Unicode if you
anyway would never help with providing anything.

>I have seen examples of both types of epsilon being used to denote set
>membership,

No doubt due to "limitations in past typesetting".

>and I have seen examples of both types of epsilon being used as
>a small number > 0. You could probably add a whole range of characters
>moving from \varepsilon to \epsilon to \in for set membership.

That's where I suspect you get it all wrong. You're talking about a whole
range of _glyphs_, in appearence similar to anything between the
\varepsilon and the \in of Computer Modern, but they're all the same
semantic atom (i.e., character) and thus shouldn't have distinct internal
representations in LaTeX. That at least part of that range of glyphs may
also be used to represent another character (the greek letter small
epsilon) which should have its own internal representation is another
matter.

>Knuth, being wise, realized how disparate the use of the symbols are in
>math, and introduced a macro symbols system so that anyone can define them

The point is that the macro system Knuth created has no internal
representation for characters, neither in text nor math---instead it is
based on the user specifying what glyph (or combination of glyphs) is
desired. LaTeX, by contrast, has an internal representation for characters
as of version 2e, but still uses the Knuthian glyph selection commands in
math. What I argue is that by version 3 of LaTeX there should be an
internal math character representation as well.

>Further, if you want to make it impossible to use \varepsilon and \epsilon
>side by side in the same document, you will have to make sure that in all
>of the world literature in the past up till now it has never been used that
>way, because that is how the requirements of Unicode were set up.

I'm not saying that it should be completely impossible to use them side by
side (even though I would question any attempts to do so), but they
shouldn't be provided as distinct characters in the default set-up.

>As for the math characters, I do not see there is any point in trying to
>impose equivalences because the way the may be used in math, and it is just
>an unnecessary additional work in implementation.

It is very little additional work in the implementation of LaTeX (adding an
OCP which normalizes the input somewhat further than what Unicode precribes
will do), but it saves much (largely unnecessary) work in the
implementation of fonts for LaTeX, and thereby it facilitates the creations
of new fonts.

Lars Hellström