The situation with {} is very similar to the situation with 0̸ for
the empty set and with \ for set subtraction. The Knuth's version of TeX
was designed for typesetting his books, and he (probably) did not
encounter situations where the meaning of these symbols is ambiguous.
When AMS was designing AmSTeX, the editors had experience with more
types of text, and knew solutions for these ambiguity problems: use
visually unique symbols \varnothing and \smallsetminus. (Frankly
speaking, this is my reconstruction; the symbols may have been
introduced earlier than AmSTeX.)
To clarify for everyone else: The important thing to realize is that the
TeXbook has only \setminus (looks like a long backslash) and \emptyset
(looks exactly like the thin German struck-through zero with thicker
vertical portions), no \varnothing ∅ or \smallsetminus ∖.
So as far as I understand, the mathematicians who would use 0̸ and \ for ∅ and
∖ are the same people who would use DOT DOT DOT for ellipsis and won't use
\mid in {x∈ℝ||x|<1}.
I'm with you in the choice of (La)TeX macro, but this should imo be more
about spacing, contextual variation (of spacing or symbol length), or
being semantically appropriate (which is imo less important than some
would want to make you think – who cares about a distinction between \to
and \rightarrow, just because for historical reasons there are now two
macros for the same thing). While I find ∅ and ∖ objectively better than
Ø (or 0̸) and \, the question raised was more about the historical glyph
development, and the choice of glyph is in principle orthogonal to
(La)TeX spacing/breaking/variation.
In my book, atomicity is a secondary consideration. As far as an
OpenType font typesets⁽¹⁾ "DOT DOT DOT" the same as "…", and the line
breaking algorithm won't break inside "DOT DOT DOT", I would be happy
with the non-atomic version.
⁽¹⁾ Well, one good application of … not covered by OpenType is to
visually distinguish "… ." from ". …". (Ellipsis inside a
sentence vs ellipsis inside a paragraph.)
Again, I agree with what you write, but "…" has always been a bit of a
mystery to me. I guess in the US-American (sub?)tradition where (some?)
authorities ask for spaced-out
. . .
. . . .
for ellipsis (with truly bizarre rules about which to choose in any
given context; look at CMOS if you are interested in their odd and
unintuitive prescriptivism about this) it makes sense to provide a
/spaced-out/ "…"-glyph (". . .") that can't linebreak (I'd need to think
about whether you'd also want a non-linebreaking ". . . ." to conform to
CMOS rules). Otherwise I don't see why dot-dot-dot shouldn't suffice.
Stephan
