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Hans Aberg <[log in to unmask]>
Wed, 9 Apr 1997 13:21:36 +0200
text/plain (82 lines)
>> Johannes Kuester <[log in to unmask]> wrote:
>> >May be there should be a fourth script-like font, or at least parts of
>> >an alphabet in such a style, to be used for some special one letter symbols,
>> >containing for example
>> >
>> >P for the power set (also mentioned in J. Ziegler's article)
>> >C to denote the set of continuous / continuous differentiable functions
>> >  (as in C^k(\mathbf{R}) or the like)
>> >O and o for the Landau symbols (denoting the order of magnitude of
>> >  a function)

I wrote:

>>   I am thinking of having perhaps only two (using NFSS terminology)
>> "scripty" families, one less scripty, like the AMSfonts Euler script, and
>> one more scripty, looking like handwritten script, which would cover those
>> symbols mentioned above, both upper/lowe case then. These families would
>> then come in full (math) series (normal, bold) and shapes (upright,
>> slanted).

>(I suppose that `handwritten script' here refers to `Formal Script'
>(e.g. rsfs fonts), is that correct?)

  I used this "handwritten script" terminology as a generic for all the
kinds of handwritten script styles in use (and these often archaic styles
are regionally so different that a person who learned one style may have
trouble reading another). Then there are typesetting variations of this: In
fact, the "rsfs" font package contains some interesting documentation on

>I'll try to be more explicit. One frequent notation of `power set'
>is to use \mathfrak{P}. Now, if Fraktur is used for e.g. vector spaces,
>this is ambiguous and should be avoided by escaping to \mathscr{P}.
>But if Formal Script is used for another concept, one has to use
>yet another symbol etc.
>  Thus I think it would be better to have a special, reserved symbol
>for `power set', clearly distinguishable from other `P's. Justin Zieglers
>proposal contained a position for such a letter (and his article some
>ASCII art to give an idea of that glyph), and WordPerfect has such a glyph
>in (one of) its character set(s), though wrongly called `Weierstrass'
>(no, it is not TeX's \wp for the Weierstrass `p' function, that glyph
>is there, too (also called `Weierstrass').

  Several symbols start off as letters, migrating to beocme independent
symbols after a while: For example the integral sign $\int$ started off as
a script letter $S$ (by Leibnitz), I think, and the empty set symbol
$\emptyset$ or $\varnothing$, is typeset as a $\phi$ in older books.

  When a letter has become a symbol, is probably up to the author to decide.

  So there are two different issues here: Treating mathematical alphabets,
and treating special symbols.

  These details are treated in the document Justin Ziegle's article, which
should be someting like /info/ltx3pub/l3d007.tex at CTAN.

  On the mathematical alphabets, fraktur is traditional. For different
"scripty" fonts, the main thing seems to be that they are clearly
distinguishable. There are some less scripty letter fonts included in the
standard \TeX and AMSfonts packages, and there seems to be the room and
need for another more scripty series. Hence my suggestion for two sets of
scripty fonts.

>Now there are more symbols with the similar problem: how to represent
>them unambiguously. May be these won't make up a whole alphabet, may be
>they shouldn't be called a font, as they need not share characteristics,
>and may be they don't need to have a script-like appearance, but all this
>doesn't change the mathematical necessity for such symbols, and I think
>that TeX should provide them (may be after a lengthy discussion about their
>appearance, as there does't seem to be a design for these symbols except
>for the power-set-P).

  Also this stuff is treated in Justin's article.

  If somebody wants to do that, it probably is a good idea to collect, and
classify, suggestions for new sets of math symbols.

  Or so I believe.

  Hans Aberg