Jim Allan wrote:
> Kent Karlsson posted on the use of slashed zero for empty set:
>
> > Yes... A horrible glyph for denoting the empty set, if I may say so.
> > No
> > offence intended. Please use the glyph available via the command
> > \varnothing (a misleading name...) in the amssymb package;
> or simply a
> > capital o with stroke (U+00D8; upright or italic) to denote
> the empty
> > set.
> > (Note that TeX is "glyph code oriented"; not really
> character oriented.)
>
> I disagree.
>
> I feel the slashed zero form better interacts typographically
> with other
> symbols than the austere slashed circle, especially in linguistics.
Perhaps. I did say "for denoting the empty set". And Pullum,
in "Phonetic symbol guide" (1996), does distinguish them.
> It is probable that appearances of the slashed capital O to mean
> nothing, null set, etc, are purposeful, not just typographical
> compromises when the correct symbol wasn't available.
(re "nothing" see below)
Probably. But it is not a good (i.e. highly conventional) way to
denote the empty set.
> Knuth certainly knew such variants but chose what he thought was the
> best one for the character. Have you any indication it was
> not then also the most normal one?
I'm not going to do any statistical occurrence analysis; but it is not
in line with the origin of the character. (It is also not the one I'm
used
to, apart from that in old typewriter-written material where 0 and O
aren't (couldn't be) different in any way...)
> The names used for these symbols in the mathml lists indicate
> that the slashed circle that is now seen as the variant form.
Another way of denoting the empty set in MathML is <mi>Ø</mi>...
(Perhaps not an expected one by the authors of the MathML
specification.)
> Slashed zero in itself suggests nothingness and emptiness better than
> slashed capital O, which probably in part explains why its
> use has spread.
Maybe. B.t.w.: nothingness and emptiness is not the same. An empty set
is a set, which is something (in an abstract sense), not a nothing.
However,
the empty set *contains* nothing, but the set of the empty set, {{}} or
{Ø},
contains the empty set (i.e. it has one element)...
However, what is used in linguistics, in reference to this discussion,
is a
denotation for the empty string (which is also something, not a
nothing).
The empty set is also used, but that is quite different from the empty
string,
and also different from the set of the empty string (which has one
element!).
> The symbol is one, and to be encoded as U+2205 pending
> indication that
> distinctions have been generally made between the glyphs or new
> standards requesting that in the future a distinction be made between
> the glyphs.
Pullum distinguishes them (as symbols). TeX (in practice) distinguishes
them (as symbols). MathML apparently wants to distinguish them. (Though
I find the slashed zero variety already representable in Unicode.)
/kent k
