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Re: Binary Relations, draft 1

>>>>> "HA" == Hans Aberg <haberg@matematik.su.se> writes:

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

Hans,

Thanks again for the trouble.

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

Currently, my "normal" triangles are actually closed versions of
"less" and "greater". So, I would then like to use the real
equilaterals as variations.

 HA> So then these should merely be renamed.

If the "var" versions have to be triangles, then they will be
triangles. But see below for a remark on triangles as operators.

If you really like having closed versions of succ and prec, that is
fine, then I will add those. On the other hand, if the wish to have
them is only an academic desire to have as many symbols as possible,
then I object. (If you want weird symbols as "on-the-fly" relations,
you might as well use a dingbat font).

 HA> AMS-fonts have \blacktriangleleft and \blacktriangleleft, which I did not
 HA> find in your table. 

forgot those (they are in my "misc" corner). Will add.
 
 HA> They also have \vDash, \Vdash, and \Vvdash, which looks
 HA> like |=, ||- and |||-. TeX has \vdash, \dashv and \models, looking as |-,
 HA> -|, and |=, and \perp. (Perhaps I missed them.)

There are a lot more like this, much more than would fit in one font,
I'm afraid. If it doesn't fit, I will add those to the next font
(which also stars about 125 negated relations) and/or shuffle some of
them around in the fonts so that both are rasonably filled. There are
quite some few negated ones because one does not have "negated
dualmap" for example.
 
 HA> On 175/176, I would want to have variations with the = negated ("not
 HA> equal") under the \subset: There is some confusion in math as to which
 HA> symbol is the subset symbol (180 or 182), so if one thinks of \subset as an
 HA> implication and not a <, this is nice to have for clarity.

All negations are to appear in the next font. 

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

Noted.

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

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

Amsfonts are (implicit apology to the ams people) *ugly*. Functional,
but very *ugly*. I will do not consider these fonts to be usable as a
reference representation of anything. But you might still be right, of
course. Will check some other fonts.

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

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

Your explanation is unclear to me. My english is not all that good. If
they *are* different, then it might be nice to design them to be
different as well. But which one of the two should be changed and how?

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

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

The table also has operators "left closed times sign" and "right
closed times sign", that really look like times with a bar on one
side. For the filled version, these are marked as "relations" instead
of operators, and those turned out as char 235 and 237.
 
 HA> In general, in the few cases where a similar symbol exist both as a binary
 HA> relation and as a binary operator (as in the case of AMS-font
 HA> \vartriangleleft and TeX \triangleleft), the relations seems to be
 HA> prolonged relative to the operator.

I also have triangle as a binop (which is equilateral, indeed). The
current variations are all flagged as relations. 

Greetings, Taco