# Re: Binary Relations, draft 1

• To: math-font-discuss@cogs.susx.ac.uk
• Subject: Re: Binary Relations, draft 1
• From: Hans Aberg <haberg@matematik.su.se>
• Date: Sun, 15 Nov 1998 21:19:46 +0100
• Content-Length: 2832

```At 17:59 +0100 1998/11/15, Taco Hoekwater wrote:
> I just uploaded a first draft
>of the font that contains the binary relations.

The symbols
037 037 22B2 vartriangleleft
038 038 22B3 vartriangleright
should definitely be triangles (straight corners). I think these together with
039 039 22B4 trianglelefteq
040 040 22B5 trianglerighteq
should be designed as the AMS-fonts
\vartriangleleft
\vartriangleright
\trianglelefteq
\trianglerighteq
that is, somewhat prolonged (not exactly an equilateral triangle). But I
see that you have 146/147: Perhaps 037/038 are closed variations of TeX
\succ and \prec; it is always nice having extra relations to choose from.
So then these should merely be renamed.

AMS-fonts have \blacktriangleleft and \blacktriangleleft, which I did not
find in your table. They also have \vDash, \Vdash, and \Vvdash, which looks
like |=, ||- and |||-. TeX has \vdash, \dashv and \models, looking as |-,
-|, and |=, and \perp. (Perhaps I missed them.)

On 175/176, I would want to have variations with the = negated ("not
equal") under the \subset: There is some confusion in math as to which
symbol is the subset symbol (180 or 182), so if one thinks of \subset as an
implication and not a <, this is nice to have for clarity.

I think that
080 080 2234 therefore
158 158 2235 because
are not binary relations, even though labeled so in the AMS-fonts.

>"closure" (233) and "asymp" (9) use the symbols from "frown" (54) and
>"smile" (55). Is that correct?

You seem to have made the "frown" (54) and "smile" (55) thicker to the
middle, as of a mouth. I think that this might be incorrect; TeX and
AMS-fonts seem to not have done that. (Most these relations seem to be
designed as sans-serif, of equal thickness.) Otherwise I think that you are
not forced to use the "frown" and the "smile" for the other two; just make
them look good.

>Is "mostpos" (5) the same shape as "ac" (224)?
>Is "congruence" (159) the same shape as "race" (222)?

For these, one can always think of the curl starting up/down, as in
222/224. But I do not know if that is how people are using them.

>The naming scheme hints that "bowtie" is a doubly closed multiplication sign.

TeX has a binary relation called \bowtie; it looks like bowtie and not as a
double close x (the bowtie is more prolonged). But I do not recall any
usage.

In general, in the few cases where a similar symbol exist both as a binary
relation and as a binary operator (as in the case of AMS-font
\vartriangleleft and TeX \triangleleft), the relations seems to be
prolonged relative to the operator.

Hans Aberg
* Email: Hans Aberg <mailto:haberg@member.ams.org>