Re: sets of sets

From: Cimode <>
Date: 30 Jul 2006 13:03:38 -0700
Message-ID: <>

This paper was discussed and proposed by Aloha in the following thread...

It is an introductary paper on ensemblist math..The paper was linked on

The point you have evoked is a direct application of Axiom of Power Set of Zermelo-Fraenkel on which I encourage you to do some serious reading for better understanding...Here is a book that may help if you want to get serious understanding of the matter...

In words (source wilkipedia)
"Given any set A, there is a set such that, given any set B, B is a member of if and only if B is a subset of A"

A direct application for RM was evocated in the thread I mentionned...

Check the below link for more info...

Hope this helps...

[Quoted] paul c wrote:
> I'm trying to read a recent paper I found at
> (The description intrigued me because the author is exploring RT. I'll
> try to contact the author with my question, but I thought I'd mention it
> here as others may be interested.)
> Anyway, at the top of page 5, he defines something I can only call
> "UNION S" (since I don't know know how to type the set union operator
> symbol).
> Can anybody suggest whether I'm reading it right? What I think it says
> in prose is "the set of x such that x is a member of some subset of S".
> Below I've tried to paste the pdf text, not sure how it will show up in
> different newsreaders, sorry for breaking the rules with a little bit of
> non-text:
> Let S be a nonempty set of sets. Then ∪S is defined as {x | ∃S′ ∈ S . x
> ∈ S′} ...
> Then he mentions what I call "INTERSECTION S" which seems to mean the
> set of x such that x is a member of all subsets of S", (text pasted
> below, I hope):
> and ∩S as {x | ∀S′ ∈ S . x ∈ S′}.
> p
Received on Sun Jul 30 2006 - 22:03:38 CEST

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