OASIS Mailing List ArchivesView the OASIS mailing list archive below
or browse/search using MarkMail.


Help: OASIS Mailing Lists Help | MarkMail Help

[Date Prev] | [Thread Prev] | [Thread Next] | [Date Next] -- [Date Index] | [Thread Index]
Re: [xml-dev] An element that contains itself

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.

[Date Prev] | [Thread Prev] | [Thread Next] | [Date Next] -- [Date Index] | [Thread Index]

News | XML in Industry | Calendar | XML Registry
Marketplace | Resources | MyXML.org | Sponsors | Privacy Statement

Copyright 1993-2007 XML.org. This site is hosted by OASIS