From: Jim Allan (jallan@smrtytrek.com)
Date: Mon Jun 02 2003 - 18:30:06 EDT
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.
The slashed circle looks good to me only when found surrounded by ony
the other austerely designed sans-serif symbols for set theory.
When the symbol was adopted for other uses and other notations, to
appear with symbols in Roman-style serif fonts, it would naturally be
typographically adapted to fit the same style.
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.
It is hard to imagine situations where a standard sans-serif Ø wasn't
available, a shape for all practical purposes indistinguishable from a
slashed circle in most fonts.
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?
The names used for these symbols in the mathml lists indicate that the
slashed circle that is now seen as the variant form.
> It would have been much better if it had been stated explicitly when
> this notation for the empty set was introduced that they were using
> the Norwegian letter for this, just as (quite ordinary) greek small pi
> and ordinary e, is used to denote specific mathematical entities.
> But alas, that was not the case, and as a result we see an unfortunate
> divergence in notation.
Those who prefer the look of the slashed zero will see the divergence in
typographical style as a fortunate divergence.
Slashed zero in itself suggests nothingness and emptiness better than
slashed capital O, which probably in part explains why its use has spread.
The difference between the glyphs is no greater than between ampersand
and ampersand.
From http://math.ucr.edu/~toby/Oz/sets/
<< Empty set: the set with no elements. Originally denoted by the
Scandivanian O with a slash through it ("Ø"), it's now more commonly
denoted as a numeral zero with a slash through it. (Anyone who tells you
it's a Greek Phi is just wrong.) Of course, you could also say "{}". I
will say "Ø" on this crib sheet. >>
That seems to be facts of the matter.
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.
Jim Allan
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