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**To**:*math-font-discuss@cogs.susx.ac.uk***Subject**:**Re: Binary Relations, draft 1****From**:*Hans Aberg <haberg@matematik.su.se>***Date**: Mon, 16 Nov 1998 13:02:21 +0100- Content-Length: 6034

At 22:56 +0100 1998/11/15, Taco Hoekwater wrote: > 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). The reasoning is like this: I am not sure that there should be equilateral triangles used as binary relations; påerhaps as operators, but not as relations. AS relations they shoudl be prolonged. They then need only look good, not be say a closed <. However, your curled 037/038 look very good. I have noted that if one writes a paper with several different relations, then it is difficult to find good variations. So from that perspective, I think a closed variation of \succ and prec should be added. > 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. This is not a negated subset, but a strict subset, so therefore it should be in this font. (One could also in principle negate the strict subset symbol.) > >> "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. The only thing that matters is that it looks good in print: When drawing by hand, I do not thionk that one does anything particular about this. > >> 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. I am also trying to learn English. :-) > 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? I only mean that a curl can always look as _ _ | |_| or |_| | starting up or down. > >> 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. For the "left closed times sign" |x and "right closed times sign" x| it is clear that these are operators, often used to denote a trivial extension in group theory, homological algebra and such theories. For completeness, one might add an operator "doubly closed times sign" |x|, even though I do not recall any use of it. These are clearly a "times sign" with extra strokes on (because that is how they arise mathematically, as a Cartesian product with some additional properties). The bowtie looks different though, being prolonged, so therfore I think it is different from the "doubly closed times sign", and that the bowtie should only be a relation, not an operator. > 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. What I mean here is that these symbol variations, binary operator/relation, are both semantically and graphically different, and when used side by side a mathematician would recognize the difference: The relation will be somewhat prolonged relative the operator. That is what the empiricism seemed to be to me. Hans Aberg * Email: Hans Aberg <mailto:haberg@member.ams.org> * Home Page: <http://www.matematik.su.se/~haberg/> * AMS member listing: <http://www.ams.org/cml/>

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