On Mon, 21 Jul 2008 20:23:13 +0100, Jack <jj@[EMAIL PROTECTED]
>
wrote in <news:zm5hk.26530$gU4.6599@[EMAIL PROTECTED]
> in
alt.algebra.help:
[...]
>> {B(x, p, q) : p, q in J & p != q}.
> What's that exclamation mark about? Is it what I type, an
> exclamation mark?
'!=' is a standard ASCII representation of the not-equals
sign. LaTaX \not=, I believe.
>>> Perhaps I just write out a new definition, "let
>>> B_{0}(x,J) be the set of sets B for a given J"?
>> I would not use B_0 as the name of a collection of sets that
>> are individually called B; script-B(x, J) would be more
>> appropriate.
> 'script-B'? What's that then?
An upper-case script letter <B>. Possibly LaTeX
\mathcal{B}.
>> <later>
>>> Actually, that won't get me what I want. I want to be able
>>> to refer to the sum of the cardinalities of all possible
>>> sets B(x,p,q).
>> If you have a name for a finite collection of sets, it's
>> trivial to talk about the sum of the cardinalities of those
>> sets. If F is a finite family of sets, the sum of the
>> cardinalities of the members of F is obviously
>> sum{|f| : f in F}.
> So with the sets B, I define my set script-B(x, J), then write
> "sum{|B(x,p,q)| : B(x,pq) in script-B"?
There are at least three errors there: a missing comma, a
missing right curly brace, and missing arguments on the name
of the collection of sets. You want:
sum{|B(x, p, q)| : B(x, p, q) in script-B(x, J)}
However, you don't actually need all of that clutter:
sum{|B| : B in script-B(x, J)}
says exactly the same thing.
> And if I want the union of all B(x,p,q), what then?
Just stick a union sign in front of script-B(x, J). I
suppose that in LaTeX this is something like
\bigcup \mathcal{B}(x, J)
(There are many other perfectly good ways to write it, but
this is the simplest.)
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