[texhax] Some questions on math mode

[Philip TAYLOR]

P. R. Stanley wrote:
> Hi folks
> 1. What effect does placing a letter [A-Za-z] in math mode produce, 
> for example $x$ $A$?

It sets the letter in maths italic, which is similar
to (but not the same as) text italics.

> 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.

I'm no mathematician (as Chris Rowley will hasten to assure
you !) but a short fragment from an LMS paper may help :

> For any non-empty subset $\mathcal I$ of the natural numbers

> 3. The same document states that the \mathbb macro can be used for 
> displaying rationals reals and so forth. Again, What visual effects 
> does the mathbb have on the enclosing character. 

It creates "blackboard bold", which looks as if the same
character had been rendered twice with a small displacement
(horizontal) between the two instances.

> I have come across 
> quite a few of those \math macros -- mathrm, mathtt and so on. It's 
> hard to know what they do or, more importantly, when they should be 
> used. Any tips would be most appreciated.

In general, the "math" prefix simply indicates that the
macro is intended for use in maths mode; the characters
that follow indicate the intended effect, such as
"rm" => "roman", meaning upright; "tt" -> "teletype",
meaning monospaced and highly stylised.  It's a great
shame that (as far as I know) no-one has yet reported
a document from whence all of these things can be
gleaned.

Philip TAYLOR