[texhax] Some questions on math mode

[P. R. Stanley]

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

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.

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. 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.

Thanks
Paul