[XML-DEV Mailing List Archive Home] [By Thread] [By Date] [Recent Entries] [Reply To This Message]

Re: An element that contains itself

• From: David Rudel <fwqhgads@gmail.com>
• To: "xml-dev@lists.xml.org" <xml-dev@lists.xml.org>
• Date: Wed, 6 Aug 2014 20:38:50 +0200

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.

• References:
  • An element that contains itself
    • From: "Costello, Roger L." <costello@mitre.org>
  • Re: An element that contains itself
    • From: Shaun McCance <shaunm@gnome.org>