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List:       xml-dev
Subject:    Re: [xml-dev] An element that contains itself
From:       David Rudel <fwqhgads () gmail ! com>
Date:       2014-08-06 18:38:50
Message-ID: CALEJ_nCYaQ5QJDkBh5ECjxCFtWJ8MuA-8LOeWWa=pGfpQP1mCA () mail ! gmail ! com
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On Wed, Aug 6, 2014 at 7:31 PM, Shaun McCance <shaunm@gnome.org> wrote:
>>
>>       A set of a collection of distinct objects,
>>       none of which is the set itself.
>
> Sorry, this just isn't true. Set are allowed to contain themselves in
> every formulation of set theory I've ever seen. Mathematicians have no
> problem whatsoever with the idea that a set contains itself.

It is true that a set is not allowed to contain itself (at least in
ZFC). That is a direct implication of the axiom of regularity.

However, at the same time, Roger's definition of a set is not
accurate. "The set of all sets" does not exist. That means "the
collection of all sets" is not a set. But if "the collection of all
sets" is not a set, then it is a collection that does not contain
itself, which would make it a set based on Roger's definition.




-- 

"A false conclusion, once arrived at and widely accepted is not
dislodged easily, and the less it is understood, the more tenaciously
it is held." - Cantor's Law of Preservation of Ignorance.

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