At 21:21 +0300 2001/05/17, Apostolos Syropoulos wrote:
>> Here are two examples:
>>   $\epsilon\varepsilon R$
>>   $\varepsilon R$
...
>I believe your example is incorrect. The right way to write the first
>formula should be:
>$\varepsilon \epsilon R$.

No, the second formula. :-) -- The correct version was zipped out by the
spell-checker I used.

The thing though is that both types of epsilon have in the past been used
to indicate set membership. In principle frequent epsilon users in say
analysis could have used the other epsilon to denote a small quantity. But
whether they actually did depends on whether they made use of set notation
and whether the epsilon's were both available by the typesetter: If some
sign wasn't available, one would have to substitute another.

Another example: TeX has undotted \imath and \jmath with the idea that they
should be used when putting math diacritical marks on top of them. But once
those symbols are there, it is possible for mathematicians to use say
\jmath and $j$ side by side. If I should conjure up an example, it is
common to let a dot denote the derivative of a path. Then, in order to
avoid confusion, one could define a path $\jmath(t)$ with derivative
$j(t)$. So then one cannot require these different versions to be
semantically equivalent anymore.

So this evolution of characters and their use in math make it difficult to
put restrictions on their usage.

  Hans Aberg