Re: Nicer S\not=\varnothing in LaTeX?
Morten Høgholm
<a...@nospam.andrew.cmu.edu> wrote:
> What LaTeX syntax do people generally use to represent the empty
> set? I have used and liked AMSLaTeX's \varnothing symbol, but the other
Empty set you say... You know, there *is* actually an \emptyset symbol. It
varies wildly between different font families though.
--
Morten Høgholm
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Lars Madsen
<moho...@smelly.student.cbs.dk> wrote:
> On Mon, 4 Oct 2004 16:30:12 -0400 (EDT), Arthur J. O'Dwyer
> <a...@nospam.andrew.cmu.edu> wrote:
>
>
>> What LaTeX syntax do people generally use to represent the empty
>> set? I have used and liked AMSLaTeX's \varnothing symbol, but the other
>
> Empty set you say... You know, there *is* actually an \emptyset symbol.
> It varies wildly between different font families though.
lol
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Morten Høgholm
<dal...@rtfsignatureimf.au.dk> wrote:
> On Mon, 04 Oct 2004 22:46:18 +0200, Morten Høgholm
> <moho...@smelly.student.cbs.dk> wrote:
>
>>
>> Empty set you say... You know, there *is* actually an \emptyset symbol.
>> It varies wildly between different font families though.
>
> lol
Actually this is not the first time I see someone asking for an empty set
symbol and only knowing about \varnothing. I wonder why... If indeed the
case is that Arthur didn't know about \emptyset (I hope I haven't come off
as being rude, Arthur).
Lars Madsen
<moho...@smelly.student.cbs.dk> wrote:
> On Mon, 04 Oct 2004 23:55:30 +0200, Lars Madsen
> <dal...@rtfsignatureimf.au.dk> wrote:
>
>> On Mon, 04 Oct 2004 22:46:18 +0200, Morten Høgholm
>> <moho...@smelly.student.cbs.dk> wrote:
>>
>>>
>>> Empty set you say... You know, there *is* actually an \emptyset
>>> symbol. It varies wildly between different font families though.
>>
>> lol
>
> Actually this is not the first time I see someone asking for an empty
> set symbol and only knowing about \varnothing. I wonder why... If indeed
> the case is that Arthur didn't know about \emptyset (I hope I haven't
> come off as being rude, Arthur).
well I didn't know \varnothing so ...
Ron Sperber
>
> [xposted to c.t.t and sci.math; f-ups to c.t.t please]
>
> What LaTeX syntax do people generally use to represent the empty set?
> I have used and liked AMSLaTeX's \varnothing symbol, but the other
> day I had cause to write
>
> S \not= \varnothing
>
> and found that on the page it just looked ugly: the two diagonal slashes
> are at different slopes, so it looks kind of like they're "falling over."
> Has anyone else ever noticed this? Does anyone think it's a problem
> worth worrying about? What alternatives do I have?
>
> (I just realized I could write S \not= \{\} instead, but I don't
> like the "empty braces" notation quite as much as the "slashed ellipse"
> notation.)
>
> TIA,
> -Arthur
I recommend using \emptyset insead of \varnothing. That may look better.
-Ron
Morten Høgholm
<a...@nospam.andrew.cmu.edu> wrote:
> I knew about \emptyset (at least, I knew non-AMS LaTeX had a symbol
> for
> the empty set, though I would have had to look up the actual name of it).
> But I recalled that it was kind of ugly. And indeed it is, at least in
> the default math font. Looks like a slashed zero; the aspect ratio is
> a bit too tall and squished for my tastes. (The AMS \varnothing has the
> opposite problem, of course, but IMVHO a little less so.)
>
> And FWIW, the slash in the slashed-zero \emptyset isn't at the same
> angle as the slash in \not=, either. I find this strange; aren't all
> the TeX math symbols supposed to be designed together as a coherent
> "typeface" like regular letters are? If so, wouldn't it be good sense
> to make the diagonal elements "match" in slope?
Designing math symbols is hard - designing negated math symbols even
harder ;-) But \emptyset isn't exactly a negated symbol is it? It is a
special/unique symbol and thus font designers haven't been so inclined to
use the normal negation symbol as a part of it.
If you look at the free (math)pazo fonts you'll see that \emptyset is a
thin perfect circle with a slash through. The also free fourier fonts has
a similar symbol although somewhat heavier. On the other hand the
commercial PAmath fonts contain a symbol quite similar to the standard CMR
symbol. Same applies to Lucida.
So as you can see, there is no clear consensus on what's "the right
design".
With respect to the negated symbols Knuth himself thought he could get
away with using \not most of the time but also realized that it didn't
work for negating certain symbols such as \in, so \notin has a different
implementation using a normal / which has a different tilt from \not.
Hillevi Gavel
> On Mon, 4 Oct 2004 20:32:37 -0400 (EDT), Arthur J. O'Dwyer
> <a...@nospam.andrew.cmu.edu> wrote:
>
>> I knew about \emptyset (at least, I knew non-AMS LaTeX had a
>> symbol for
>> the empty set, though I would have had to look up the actual name of it).
>> But I recalled that it was kind of ugly. And indeed it is, at least in
>> the default math font. Looks like a slashed zero; the aspect ratio is
>> a bit too tall and squished for my tastes. (The AMS \varnothing has the
>> opposite problem, of course, but IMVHO a little less so.)
>>
>> And FWIW, the slash in the slashed-zero \emptyset isn't at the same
>> angle as the slash in \not=, either. I find this strange; aren't all
>> the TeX math symbols supposed to be designed together as a coherent
>> "typeface" like regular letters are? If so, wouldn't it be good sense
>> to make the diagonal elements "match" in slope?
According to one of my books (Grimaldi's Discrete and Combinatorial
Mathematics, I think), the symbol representing the empty set is supposed
to be the Norwegian letter \O, that is: a variation on the letter O
(signifying the same sound as the letter \"O). So it makes more sense to
compare it to that letter in the font used than to negated symbols.
Hillevi Gavel
Department of mathamatics and physics
Mälardalens Högskola
Sweden
Lee Rudolph
...
>According to one of my books (Grimaldi's Discrete and Combinatorial
>Mathematics, I think), the symbol representing the empty set is supposed
>to be the Norwegian letter \O, that is: a variation on the letter O
>(signifying the same sound as the letter \"O). So it makes more sense to
>compare it to that letter in the font used than to negated symbols.
The following quotation-within-a-quotation is grabbed from the
useful site http://members.aol.com/jeff570/set.html (I have
replaced Unicode with TeX, since this newsreader won't let me
post highbit symbols).
---begin quotation----
The null set symbol \O first appeared in N. Bourbaki
\'El\'ements de math\'ematique Fasc.1: Les structures
fondamentales de l'analyse; Liv.1: Theorie de ensembles.
(Fascicule de resultants) (1939): "certaines propri\'et\'es...
ne sont vraies pour aucun \'el\'ement de E... la partie qu'elles
d\'efinissent est appel\'e la partie vide de E, et design\'ee par
la notation \O." (p. 4.)
Andr\'e Weil (1906-1998) says in his autobiography that he was
responsible for the symbol:
Wisely, we had decided to publish an installment establishing
the system of notation for set theory, rather than wait for
the detailed treatment that was to follow: it was high time
to fix these notations once and for all, and indeed the ones
we proposed, which introduced a number of modifications to
the notations previously in use, met with general approval.
Much later, my own part in these discussions earned me the
respect of my daughter Nicolette, when she learned the symbol
\O for the empty set at school and I told her that I had been
personally responsible for its adoption. The symbol came from
the Norwegian alphabet, with which I alone among the Bourbaki
group was familiar.
The citation above is from page 114 of Andr\'e Weil's
The Apprenticeship of a Mathematician, Birkhaeuser Verlag,
Basel-Boston-Berlin, 1992. Translated from the French by Jennifer
Gage. The citation was provided by Julio Gonz\'alez Cabill\'on.
This letter is used in the Norwegian, Danish and Faroese alphabets.
---end quotation---
So apparently Grimaldi is spot on.
Lee Rudolph
Robin Fairbairns
> This message is in MIME format. The first part should be readable text,
> while the remaining parts are likely unreadable without MIME-aware tools.
[sigh]
> I knew about \emptyset (at least, I knew non-AMS LaTeX had a symbol for
>the empty set, though I would have had to look up the actual name of it).
>But I recalled that it was kind of ugly. And indeed it is, at least in
>the default math font. Looks like a slashed zero; the aspect ratio is
>a bit too tall and squished for my tastes. (The AMS \varnothing has the
>opposite problem, of course, but IMVHO a little less so.)
>
> And FWIW, the slash in the slashed-zero \emptyset isn't at the same
>angle as the slash in \not=, either. I find this strange; aren't all
>the TeX math symbols supposed to be designed together as a coherent
>"typeface" like regular letters are? If so, wouldn't it be good sense
>to make the diagonal elements "match" in slope?
sounds an inherently sensible idea.
however, the crossing of the <whatever> in an empty set symbol
actually has a different semantic to the crossing of \not. i'm sure
knuth could rustle up several arguments as to why the slopes don't
match.
--
Robin (http://www.tex.ac.uk/faq) Fairbairns, Cambridge
Morten Høgholm
> "Arthur J. O'Dwyer" <a...@nospam.andrew.cmu.edu> writes:
>> This message is in MIME format. The first part should be readable
>> text,
>> while the remaining parts are likely unreadable without MIME-aware
>> tools.
>
> [sigh]
Hmm. Apparently Opera shows me only what I want to see.
> however, the crossing of the <whatever> in an empty set symbol
> actually has a different semantic to the crossing of \not. i'm sure
> knuth could rustle up several arguments as to why the slopes don't
> match.
Given that the symbol should in fact be Ø (\O) according to other parts of
this thread, it'd be quite interting to hear the arguments ;-)
Morten Høgholm
wrote:
> According to one of my books (Grimaldi's Discrete and Combinatorial
> Mathematics, I think), the symbol representing the empty set is supposed
> to be the Norwegian letter \O, that is: a variation on the letter O
> (signifying the same sound as the letter \"O). So it makes more sense to
> compare it to that letter in the font used than to negated symbols.
Just asked a Danish algebra wizard (Frank Hansen) I know and he confirms
this. Most insteresting...
Robin Fairbairns
>On 5 Oct 2004 13:01:22 GMT, Robin Fairbairns <r...@cl.cam.ac.uk> wrote:
>> however, the crossing of the <whatever> in an empty set symbol
>> actually has a different semantic to the crossing of \not. i'm sure
>> knuth could rustle up several arguments as to why the slopes don't
>> match.
>
>Given that the symbol should in fact be Ø (\O) according to other parts of
>this thread, it'd be quite interting to hear the arguments ;-)
one lives and learns. (come to think of it, i can't remember what
whitehead and russell used -- that's where i took my first steps in
set theory.)
anyway, knuth has danish ancestry, doesn't he? perhaps he knew what
he was doing, even?
Harald Hanche-Olsen
| [...] the symbol representing the empty set is supposed to be the
| Norwegian letter \O, that is: a variation on the letter O
| (signifying the same sound as the letter \"O). So it makes more
| sense to compare it to that letter in the font used than to negated
| symbols.
Well, having grown up with the letter Ø (\O) and later with \emptyset,
I have never thought of them as identical, only similar - in the same
sense that the digit 0 and the letter O are similar. In particular,
it would never occur to me to read \emptyset aloud as Ø. Accordingly,
I much prefer that the two symbols are quite distinct
typographically. That André Weyl modelled \emptyset on the letter Ø
is an amusing anecdote and nothing more, IMNSHO.
--
* Harald Hanche-Olsen <URL:http://www.math.ntnu.no/~hanche/>
- Debating gives most of us much more psychological satisfaction
than thinking does: but it deprives us of whatever chance there is
of getting closer to the truth. -- C.P. Snow
Harald Hanche-Olsen
| anyway, knuth has danish ancestry, doesn't he? perhaps he knew what
| he was doing, even?
I don't know, but he spent some time in Oslo (maybe on sabbatical
leave) so he was certainly familiar with the Norwegian/Danish alphabet
when he designed the CM fonts.
Jellby
> According to one of my books (Grimaldi's Discrete and Combinatorial
> Mathematics, I think), the symbol representing the empty set is supposed
> to be the Norwegian letter \O, that is: a variation on the letter O
> (signifying the same sound as the letter \"O). So it makes more sense to
> compare it to that letter in the font used than to negated symbols.
I have always thought of the empty set symbol as a set (Venn diagram)
crossed out, meaning, quite intuitively for me, that the set is empty.
The fact that it was originally meant to be a letter "ø" doesn't mean it has
to be typeset as such. The integral sign, for instance, was originally an
S, but it's not typeset as a standard S. It could be that the letter "ø"
was chosen because it resembled a simple stroken circle...
--
Ignacio __ Fernández Galván
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Dan Luecking
<a...@nospam.andrew.cmu.edu> wrote:
>
>On Tue, 5 Oct 2004, [iso-8859-15] Morten Høgholm wrote:
>>
>> Actually this is not the first time I see someone asking for an empty set
>> symbol and only knowing about \varnothing. I wonder why... If indeed the
>> case is that Arthur didn't know about \emptyset (I hope I haven't come
>> off as being rude, Arthur).
>
>No problem. :)
>
> I knew about \emptyset (at least, I knew non-AMS LaTeX had a symbol for
>the empty set, though I would have had to look up the actual name of it).
>But I recalled that it was kind of ugly. And indeed it is, at least in
>the default math font. Looks like a slashed zero; the aspect ratio is
>a bit too tall and squished for my tastes. (The AMS \varnothing has the
>opposite problem, of course, but IMVHO a little less so.)
The mathabx package has a \diameter symbol similar to \varnothing, but
with slightly less slant.
The diagonal element in \emptyset is clearly designed to go well with
0 (zero) it crosses. Other symbols have diagonal elements that don't
match \not in slope. The minute you change that slope to match \not,
you will find it doesn't match \notin, which has a different slope
for reasons already mentioned.
Dan
--
Dan Luecking Department of Mathematical Sciences
University of Arkansas Fayetteville, Arkansas 72701
To reply by email, change Look-In-Sig to luecking
David Kastrup
> The fact that it was originally meant to be a letter "ø" doesn't
> mean it has to be typeset as such. The integral sign, for instance,
> was originally an S, but it's not typeset as a standard S. It could
> be that the letter "ø" was chosen because it resembled a simple
> stroken circle...
Or it might have been chosen because some people use something quite
similar to it as fillin material void of meaning when talking.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
UKTUG FAQ: <URL:http://www.tex.ac.uk/cgi-bin/texfaq2html>
Giuseppe Bilotta
> On Tue, 05 Oct 2004 14:41:53 +0200, Hillevi Gavel <hillev...@mdh.se>
> wrote:
>
> > According to one of my books (Grimaldi's Discrete and Combinatorial
> > Mathematics, I think), the symbol representing the empty set is supposed
> > to be the Norwegian letter \O, that is: a variation on the letter O
> > (signifying the same sound as the letter \"O). So it makes more sense to
> > compare it to that letter in the font used than to negated symbols.
>
> Just asked a Danish algebra wizard (Frank Hansen) I know and he confirms
> this. Most insteresting...
It would be interesting to know why that letter was chosen.
Maybe some Irish guy reading ömpty set instead of empty set? ;)
(Sorry, couldn't resist; still thinking of the day I played
dictionary with an Irish guy and he asked if the word was
"mouse", read "mois" :))
--
Giuseppe "Oblomov" Bilotta
Can't you see
It all makes perfect sense
Expressed in dollar and cents
Pounds shillings and pence
(Roger Waters)
David Cameron Staples
<bilo...@hotpop.com>) in hoc locus scripsit:
> Morten Høgholm wrote:
>> On Tue, 05 Oct 2004 14:41:53 +0200, Hillevi Gavel
>> <hillev...@mdh.se> wrote:
>>
>> > According to one of my books (Grimaldi's Discrete and Combinatorial
>> > Mathematics, I think), the symbol representing the empty set is
>> > supposed to be the Norwegian letter \O, that is: a variation on the
>> > letter O (signifying the same sound as the letter \"O). So it makes
>> > more sense to compare it to that letter in the font used than to
>> > negated symbols.
>>
>> Just asked a Danish algebra wizard (Frank Hansen) I know and he
>> confirms this. Most insteresting...
>
> It would be interesting to know why that letter was chosen. Maybe some
> Irish guy reading ömpty set instead of empty set? ;)
>
> (Sorry, couldn't resist; still thinking of the day I played dictionary
> with an Irish guy and he asked if the word was "mouse", read "mois" :))
Orthography joy. I first read that in Gaelic orthography, where 'mois' is
pronounced [mosh]. I would have put his pronunciation as 'moice', to rhyme
with 'Rolls-Royce'. (Or for those who watch Australian TV, Kath & Kim
saying 'noice' for 'nice'.)
I have a soft spot for the Northern Irish accent's pronunciation of the
long 'a' as [ai-je], hence 'face' becomes [fay-yes], but that's just me.
--
David Cameron Staples | staples AT cs DOT mu DOT oz DOT au
Melbourne University | Computer Science | Technical Services
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Michael Mair
David Cameron Staples wrote:
> In Wed, 06 Oct 2004 00:24:36 +0200, Giuseppe Bilotta (Giuseppe Bilotta
> <bilo...@hotpop.com>) in hoc locus scripsit:
>
>>Morten Høgholm wrote:
>>
>>>On Tue, 05 Oct 2004 14:41:53 +0200, Hillevi Gavel
>>><hillev...@mdh.se> wrote:
>>>
>>>>According to one of my books (Grimaldi's Discrete and Combinatorial
>>>>Mathematics, I think), the symbol representing the empty set is
>>>>supposed to be the Norwegian letter \O, that is: a variation on the
>>>>letter O (signifying the same sound as the letter \"O). So it makes
>>>>more sense to compare it to that letter in the font used than to
>>>>negated symbols.
>>>
>>>Just asked a Danish algebra wizard (Frank Hansen) I know and he
>>>confirms this. Most insteresting...
>>
>>It would be interesting to know why that letter was chosen. Maybe some
>>Irish guy reading ömpty set instead of empty set? ;)
>>
>>(Sorry, couldn't resist; still thinking of the day I played dictionary
>>with an Irish guy and he asked if the word was "mouse", read "mois" :))
>
> Orthography joy. I first read that in Gaelic orthography, where 'mois' is
> pronounced [mosh]. I would have put his pronunciation as 'moice', to rhyme
> with 'Rolls-Royce'. (Or for those who watch Australian TV, Kath & Kim
> saying 'noice' for 'nice'.)
>
> I have a soft spot for the Northern Irish accent's pronunciation of the
> long 'a' as [ai-je], hence 'face' becomes [fay-yes], but that's just me.
Having played something like dictionary with someone from Northern
Ireland, I fondly recall:
"Is it ahnoil?" "??? I guess no..."
...[Couple of minutes later] ...
"Did you mean 'an owl'?" "That's what I said... ahn oil..."
*g*
Cheers
Michael
Jellby
>> It could
>> be that the letter "ø" was chosen because it resembled a simple
>> stroken circle...
>
> Or it might have been chosen because some people use something quite
> similar to it as fillin material void of meaning when talking.
Errrr... what do you mean? ;-)
Robin Fairbairns
>Among other things, Hillevi Gavel wrote:
>> According to one of my books (Grimaldi's Discrete and Combinatorial
>> Mathematics, I think), the symbol representing the empty set is supposed
>> to be the Norwegian letter \O, that is: a variation on the letter O
>> (signifying the same sound as the letter \"O). So it makes more sense to
>> compare it to that letter in the font used than to negated symbols.
>
>I have always thought of the empty set symbol as a set (Venn diagram)
>crossed out, meaning, quite intuitively for me, that the set is empty.
>
>The fact that it was originally meant to be a letter "ø" doesn't mean it has
>to be typeset as such. The integral sign, for instance, was originally an
>S, but it's not typeset as a standard S. It could be that the letter "ø"
>was chosen because it resembled a simple stroken circle...
the integral sign remains fairly close to the shape of s at the time
it was designed. our problem here would seem to be that the nordic
people don't seem to want to change their typographic traditions; give
it another century or so, and this discussion will seem wonderfully
quaint.
Morten Høgholm
<a...@nospam.andrew.cmu.edu> wrote:
> Certainly the mathpazo \emptyset doesn't seem to "fit in" with the
> other symbols on that page, does it? It's much lighter and the line has
> a uniform thickness instead of being "stroked" (sorry, I'm not much of a
> typographer;) .
I agree with your observations.
>> With respect to the negated symbols Knuth himself thought he could get
>> away with using \not most of the time but also realized that it didn't
>> work for negating certain symbols such as \in, so \notin has a
>> different implementation using a normal / which has a different tilt
>> from \not.
>
> I see. But would \not= really look that awful if \not used the same
> slope as \notin, then? :)
Well... I guess Don didn't like the look. The reason may well be that \not
works best with relations of a certain width such as <, \simeq, etc. while
in the case of \in, the relation is too narrow for \not to blend well with
it. Thus a steeper slope is needed.
Other font designers have thought that every negated symbol should be
designed, i.e., no composite symbols - the px/txfonts by Young Ryu are
examples of that (but they have problems speaking against their use
though).