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Topic: Matheology � 261
Replies: 7   Last Post: May 10, 2013 11:39 PM

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 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Matheology § 261
Posted: May 10, 2013 9:28 PM

On May 11, 10:56 am, Zeit Geist <tucsond...@me.com> wrote:
> On Friday, May 10, 2013 4:57:08 PM UTC-7, Graham Cooper wrote:
> > On May 10, 11:10 am, Zeit Geist <tucsond...@me.com> wrote:
>
> > > ...
>
> > > I somewhat agree with the above assessment by G & N.  Finding the solution and
>
> > > correcting the problem by avoidance are two different procedures.
>
> > > ...
>
> > > When Hilbert sought to formalize set theory, and thus all of mathematics, the project
>
> > > did not include all of logic but only that was mathematical.  This set, U, constructed
>
> > > from unions of powersets of union of powersets of unions of powersets of ... and then
>
> > > the union of all of that, must be everything "producable" from those operations.
>
> > > Since U is "producable", U must be a set. Hence, we can take the powerset of U and
>
> > > "produce" something not in U.
>
> > this is a naive copycat proof of |PS(N)| > |N|
>
> > before you said such a proof is irrelevant.
>
> > CANTORS POWERSET PROOF
>
> > | CARDINALITY | > | INFINITY |
>
> > IF SET1 has 1 - then MYSET skips 1
>
> > or
>
> > IF SET1 skips 1 - then MYSET has 1
>
> > AND
>
> > IF SET2 has 2 - then MYSET skips 2
>
> > or
>
> > IF SET2 skips 2 - then MYSET has 2
>
> > AND
>
> > IF SET3 has 3 - then MYSET skips 3
>
> > or
>
> > IF SET3 skips 3 - then MYSET has 3
>
> > AND
>
> > IF SET4 has 4 - then MYSET skips 4
>
> > or
>
> > IF SET4 skips 4 - then MYSET has 4
>
> > ...
>
> > > Does this mean there is a problem with the theory? Not really, what is says is
>
> > > that U can not be treated as a set.  The problem only arises, when we treat U as
>
> > > A set.
>
> > Is there a predicate that defines U?
>
> > E(U) A(S) SeU
>
> > Can you formulaically infer values of set membership of U?
>
> > Herc
>
> Actually it's a prof the "set of all sets" is not a set.
> If it were it would to a contradiction.
>
> ZG

No it doesn't.

It's just p(X)<->true

in Naive Set theory.

E(S) A(X) XeS <-> p(X)

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