On Mon, 21 Jul 2008 15:19:25 +0100, Jack <jj@[EMAIL PROTECTED]
>
wrote in <news:LV0hk.20015$WX2.9336@[EMAIL PROTECTED]
> in
alt.algebra.help:
> "Brian M. Scott" <b.scott@[EMAIL PROTECTED]
> wrote in message
> news:ldt3l7najjfj.7f3iq4q1vwp6$.dlg@[EMAIL PROTECTED]
>> On Sat, 19 Jul 2008 22:54:47 +0100, Jack <jj@[EMAIL PROTECTED]
>
>> wrote in <news:ootgk.39471$7B3.17188@[EMAIL PROTECTED]
> in
>> alt.algebra.help:
[...]
>>> What, then, is the best way to convey that all integers in
>>> B are in [1,(y+1/2)]?
>> That's a new condition that wasn't present in your original
>> definition. If that's what you want, then I'd return to a
>> slightly modified version of the previous definition:
>> B(x, p, q) = {b in [1, x] : p | x + b or q | x - b}.
> OK -- and could you advise me as to how I should reference
> B when I am taking every member of J as a value p and
> also every member of J as a value q?
You still haven't explained what you mean by this.
> 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}.
> 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.
<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}.
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