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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**: 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> * Home Page: <http://www.matematik.su.se/~haberg/> * AMS member listing: <http://www.ams.org/cml/>

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