Brian,
>> In other words, the set of sets B for a given J?
>
> Is *that* what you were trying to convey? Ye gods and
> little fishes. That's simply {B(x, p, q) : p, q in J} if
> you allow sets B(x, p, q) with p = q; if not, then it's
> {B(x, p, q) : p, q in J & p != q}.
>
What's that exclamation mark about? Is it what I type, an exclamation
mark?
>> 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?
>
> <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"?
And if I want the union of all B(x,p,q), what then?
With thanks.
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