[texhax] Some questions on math mode

[Benjamin Sambale]

mathcal is often used to define sets consisting of sets. A typical 
example is the set of equivalence classes of a equivalence relation.

Philip TAYLOR schrieb:
> 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
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