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**To**:*math-font-discuss@cogs.susx.ac.uk***Subject**:**Re: Binary Relations, draft 1****From**:*Taco Hoekwater <taco.hoekwater@wkap.nl>***Date**: Mon, 16 Nov 1998 17:36:40 +0100 (W. Europe Standard Time)- Content-Length: 4160

>>>>> "HA" == Hans Aberg <haberg@matematik.su.se> writes: >> 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. HA> The reasoning is like this: I am not sure that there should be equilateral HA> triangles used as binary relations; perhaps as operators, but not as HA> relations. HA> AS relations they shoudl be prolonged. They then need only look good, not HA> be say a closed <. Just happened to be convenient. HA> However, your curled 037/038 look very good. I have HA> noted that if one writes a paper with several different relations, then it HA> is difficult to find good variations. So from that perspective, I think a HA> closed variation of \succ and prec should be added. OK, that will look a little different (prolonged, of course). We are left with the question whether the equilateral triangles are relations or operations, with a "probably not" as temporary answer. Building on that, we would like to have a variation on the triangles as binary relations, and these probably should look like closed succ and prec. (with the advantage that these can never be confused with the equilateral triangle operators). Am I correct? 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> This is not a negated subset, but a strict subset, so therefore it should HA> be in this font. (One could also in principle negate the strict subset HA> symbol.) I see. But I am running out of room in this font, so some stuff *has* to be moved into the negations font, which is half-empty. The idea behind these two fonts is that I can put the negated versions of various relations in the same slot in that other font. But not all relations can be (or hardly ever are) negated, so there is quite a lot of room left. It makes sense to add the overflow characters into these slots. >> >> 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. HA> 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? HA> I only mean that a curl can always look as HA> _ _ HA> | |_| or |_| | HA> starting up or down. Both of the pairs are completely identical in rendering at the moment. The symbols have descriptions to go with them, and these descriptions are: mostpos (5) : most positive [inverted lazy S] ac (224): most positive this hints that both are the same character, and one should be removed. congruence (159): congruence sign (lazy S) race (222): reverse most positive, line below this is less clear. is the "reverse most positive" something different from "congruence sign"? If so, there may have to be a difference in the rendering too, to avoid confusion. HA> These are clearly a "times sign" with extra strokes on (because that is how HA> they arise mathematically, as a Cartesian product with some additional HA> properties). The bowtie looks different though, being prolonged, so HA> therfore I think it is different from the "doubly closed times sign", and HA> that the bowtie should only be a relation, not an operator. This is clear enough for bowtie and the closed times. But there are characters 235 and 237 (left filled times and right filled times), and these are flagged as relations. If I understand you right, they should probably be operators, and removed from this font. Greetings, Taco

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