Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: set builder notation
Replies: 12   Last Post: Aug 24, 2013 1:38 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Graham Cooper

Posts: 4,253
Registered: 5/20/10
Re: set builder notation
Posted: Aug 19, 2013 1:20 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sunday, August 18, 2013 6:21:12 PM UTC-7, Seymour J. Shmuel Metz wrote:
> at 11:30 AM, dullrich@sprynet.com said:
>

> >(2) {x | x in A and P(x)}.
>
>
>

> >No:
>
>
>

> >No, because (2) is actually not a "legal"
>
> >construction of a set!
>
>
>
> It may not be legal in ZF, but it's perfectly legal in, e.g., NF. Of
>




S = { x | xeZ & p(x) }


Obviously this is going to create a hierarchy of subsets..
that cannot directly form contradictions... ala ZFC






A much simpler resolution to Russell's Set is to declare consistency.

[THEOREM 1]
ALL(T):THEOREMS T





The Theory needs some declaration to distinguish FALSE WFF from TRUE WFF.


Using Set Specification with p(X)<->X~eX
just results in a FALSE WFF.. a failed specification attempt.


EXIST(SET)ALL(X) XeSET<->p(X) -->[T|F]



Just demote SET SPECIFICATION to a WFF not a theorem.

Herc
--
www.phpPROLOG.com



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.