On 05/15/2001 at 03:04 PM, Lars Hellström <[log in to unmask]>
wrote:
>I math fonts something like that could be used to handle the choice
>between \epsilon and \varepsilon. As I understand it, these are
>semantically equivalent---i.e., people will think you've done something
>wrong if you try to use them both in the same formula to mean different
>things

On Wed, 16 May 2001, Phil Parker wrote:
>Some might, but most (at least in the parts of math I read) wouldn't.

The \epsilon and \varepsilon are definitely semantically different in
(pure) math,

At 17:51 +0430 2001/05/17, Roozbeh Pournader wrote:
>Well, with the latest version of Unicode, 3.1, \varepsilon is a different
>thing from \epsilon.

and this is the reason they are different in Unicode. (Or rather, perhaps
the STIX people took it directly out of the TeX book, but according to the
Unicode rule that semantically different symbols should have different
entries, these two epsilon forms should have different representation in
Unicode.)

Phil Parker wrote:
> The general rule of thumb seems to be: if they look different, they are
> (mathematically) different.

To a high degree this is so, but especially in the past, characters may
have looked different simply because one couldn't find the right ones.

This was the case for example when trying to make a choice between
\varepsilon and \epsilon when typewriting a manuscript. For example, IBM's
typewriter symbol head did not supply both.

>> Before the standardization of the \in
>> symbol, \epsilon was used to mean "is an element of" -- and sometimes to
>> also be the classical analysis "epsilon" in the same formula!

I think you might find old books also using \varepsilon indicating set
membership.

So just go ahead and use \epsilon and \varepsilon in the same formula.

Phil Parker wrote:
>Before the standardization of the \in
>symbol, \epsilon was used to mean "is an element of" -- and sometimes to
>also be the classical analysis "epsilon" in the same formula!

You could also try use $i$ in the same formula indicating both a summation
index and sqrt(-1) to see how people react. :-) If they don't like it, a
possibility is to typeset the imaginary unit in an upright font, and the
summation index in an oblique font.

It is important to note however that the math character set is not constant
but evolving, and the use is not even always logical in the formal sense of
logic.

  Hans Aberg
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