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

>It is true that they have distinct code points in Unicode, but so does many
>other glyphic variants of math symbols (such as U+2208, ELEMENT OF, and
>U+220A, SMALL ELEMENT OF) for which there are no distinct representations
>in LaTeX today.

You will have to check with a reply from the STIX group.

But I figure that they have attempted to add all the symbols that they can
find reasonable evidence in the present and past literature, plus a few
more in order to try to cover up for limitations in past typesetting.

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

> Furthermore the only other symbol which appears under the
>same heading as the second Unicode epsilon (U+03F5 GREEK LUNATE EPSILON
>SYMBOL, which looks like TeX's \epsilon in the code charts) is U+03F4
>(GREEK CAPITAL THETA SYMBOL), whose only difference to the proper Theta
>U+0398 (GREEK CAPITAL LETTER THETA) is that the horizontal line goes all
>the way to the ring. Is that a reason to give this variant \Theta glyph its
>own internal representation in LaTeX? I don't think so.

Whatever the construction is now in Unicode, if \epsilon and \varepsilon
both appears in TeX as distinct symbols, they should be so in Unicode,
because one took all the math symbols in TeX and added them to Unicode.

I know that in some cases there were misses, because I posted the question
to the sci.math.research newsgroup, and I recall some such misses were
subsequently pointed out.

There are further misses to Unicode, for example, I think the math font
styles are not complete, lacking European style script, and it was wrong to
add a math monospace font. But it probably not easy to fix such things.

These processes are no theoretical ideals, but highly practical processes.

>Recall that the Symbol font (which should rank as one of the more important
>sources of mathematical symbols after Computer Modern) only contains one
>epsilon glyph; thus you cannot in a math font set-up based on that font
>provide visually distinct renderings of \epsilon and \varepsilon. Then it
>is better have one command \epsilon and use some other mechanism for
>selecting how it should be rendered, if the font set-up provides
>alternative ways of rendering it.

You could add many other misses in the past in fonts: \sigma and \varsigma,
\phi and \varphi.

Therefore, one tries in Unicode to make them all available in order to
avoid these past problems.

Those old faulty font will have to be redesigned.

>Finally, a theory about the origin of the two epsilons in Computer Modern.
>While doing some checks in pre-TeX literature on mathematical typography, I
>came across the following piece of text ending a paragraph that discussed
>how one distinguishes between (what would be TeXified as) \varepsilon and
>\in:
>
>  An additional complication is that, particularly in manuscripts in
>  English, the sign $\epsilon$ does not necessarily mean $\in$, instead
>  it can just as well mean $\varepsilon$, since this letter has a more
>  grotesque'' shape in English typefaces.

I have seen examples of both types of epsilon being used to denote set
membership, 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. Further,
contemporary literature describing grammars may use either type to denote
the empty transition.

So some use them this way, and other use them the other way. Even if they
never use them side by side in the same manuscript, some may become upset
by suddenly not being able to use what they formerly have used.

>[My translation and TeXification, assuming CM math.] With such a
>traditional difference between English and, say, continental European
>typographical traditions, it wouldn't be surprising if Knuth included
>\varepsilon to please mathematicians who were accustomed to having the
>epsilon letter and set membership symbol more distinct than \epsilon and
>\in are in Computer Modern. Perhaps someone who has a copy of the book
>Computer Modern Typefaces can verify or dismiss this theory.

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

So you can redefine your \in to be say \varepsilon if that is what you
happen to prefer, even though it might look awful or be unreadable to
others.

Unicode does not try to impose conditions on the uses of the characters,
only to provide them. If LaTeX should support Unicode, LaTeX will be stuck
with the same  principle as far as math a characters is concerned.

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.

If I should tie this up so the original problem, the development of LaTeX
and TeX successor, then the TeX successor will likely be using some form of
32 bit padded characters with Unicode in the bottom. The future LaTeX will
in the future be using that. This picture gives room for future extensions,
but it will difficult to impose restrictions, because it will hurt
backwards compatibility.

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.

Hans Aberg