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**To**:*Taco Hoekwater <taco.hoekwater@wkap.nl>***Subject**:**Re: Binary Relations, draft 1****From**:*Hans Aberg <haberg@matematik.su.se>***Date**: Mon, 16 Nov 1998 19:28:55 +0100**Cc**:*math-font-discuss@cogs.susx.ac.uk*- Content-Length: 3610

At 17:36 +0100 1998/11/16, Taco Hoekwater wrote: > HA> I think that the blackboard bold characters should be added to >Unicode, for > HA> the reason that they are used in mathematics as symbols with semantic > HA> meaning, and not as a special style font. For example, it is pretty much > HA> standard to use blackboard bold R, Z denoting the sets of reals and > HA> integers, and it is becoming to be more common to use say blackboard bold > HA> small letters to denote certain fixed objects (such as blackboard bold i, > HA> j, k to denote the imaginary units in quaternions). > >They are all included in the submission tables. But they are separate >from the geometrical symbols (at least in the source) in the sense >that they are very much tied in with the text font. Using CM >Blackboard next to Times is ugly. This does not matter much, because when letters are used in math mode, they are typeset with extra space around, so that they stand out singly. So strictly speaking, the submission should have a special set of regular letters, plus the undotted i,j, for mathematical use to indicate individual mathematical variables -- that is, if one should keep the idea "one character = one meaning". On the contrary, abbreviated names, such as "sin", "cos", "Hom", "Ext", and so on, are typeset as regular text words (more densely, using ligatures), with a style (upright/slanted, sans serif/serif, bold/non-bold) added. >The included alphabets in the submission are "BlackBoard", "Script" >and "Fraktur", btw. I will probably design (or steal/borrow) a >"Calligraphic" as well. They are the very last thing on my list, >because there are no problems with the meanings (A blackboard R is a >blackboard R), so most of the time will be spent in the real design >(which will be rather tricky), instead of on discussions. We need the >discussions for almost anything else, so it was safer to do those >first (more time == more discussion == less chances of mistakes). The question on what different math styles to use was discussed in the LaTeX3 project group. I was able to identify more styles that mathematicians want to use than is currently available in TeX/AMS-fonts: First there is a regular font like times with serifs, coming in styles upright/italics, bold/non-bold. The there is a sans serif font, like helvetica, also coming in styles upright/slanted, bold/non-bold. (A total of eight variations.) Then there are the "BlackBoard Bold" and the "Fraktur", which only comes in one variation each, as alternatives do not look good. (A total of two variations.) Then, for the script fonts, there appears two variations, as you say: The AMS-fonts "American style" Calligraphic, which is not so scripty, and the "European style" Script, which is a great deal more scripty. I think that the latter one is in reality a variation of the handwritten script used in some European countries. Then these two type of script fonts should exist both as non-bold (plain) and bold. (A total of four variations.) So, summing it up, there should be a total of fourteen of these _letters_. As for the numbers and some common symbols, I do not know: These might be needed in bold/non-bold variations for some purposes, but I do not think that the other styles are used in mathematics. Some may want to use Blackboard Bold numbers, I think, but I doubt it is used for the other fonts. 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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