[texhax] Some questions on math mode

[Uwe Lück]

At 17:14 01.03.09, Benjamin Sambale wrote:
>mathcal is often used to define sets consisting of sets.

... or of *proper classes*, consisting of sets, not being sets themselves 
("too large", "contradictory").

A similar use is for *categories* in Category Theory, which often are 
"proper class versions" of relational structures whose underlying "sets" 
are proper classes indeed.

In Model Theory (belonging to Mathematical Logic) caligraphic letters quite 
consistently refer to "relational structures"; $\mathcal{A}$ may denote a 
relational structure consisting of an underlying set $A$ and subsets of 
multiple cartesian products of $A$ with itself.

I just see Paul's question on the power set: right, this may be the most 
common use!
(besides Fraktur, somewhat like with imaginary vs. real numbers.)

> > P. R. Stanley wrote:
> >> 2. The \mathcal macro displays the enclosed character in caligraph
> >> fond. According to the document at
> >> http://www.math.uiuc.edu/~hildebr/tex/course/intro2.html
> >> It says that it's used "often to denote sets". What sort of sets?
> >> Some more information on the effects of the mathcal macro on the
> >> enclosed character plus it's uses would be appreciated.

The effect is "calligraphic" [two `l'] letters, you also say "script style" 
[vs. \scriptstyle!??], looking like uppercase letters painted with a brush 
[right?]

Hope This Is True -- Uwe.