Date: May 10, 2013 11:39 PM Author: Hercules ofZeus Subject: Re: Matheology § 261 On May 11, 1:08 pm, Zeit Geist <tucsond...@me.com> wrote:

> On Friday, May 10, 2013 6:28:29 PM UTC-7, Graham Cooper wrote:

> > 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)

>

> > -------

>

> > All your contradictions are self imposed and

>

> > lead to worse atrocities such as E(X) X>oo

>

> I do t use naive set theory as it is inconsistent.

only over purely syntactically constructed WFF

with the property phi v ~phi

A WFF with the Stipulation phi XOR ~phi

N.S.T. works fine! (a variation thereof)

The CONTRADICTION

rer <-> ~(rer)

is embedded (contained ***) in a sub-formula and E(r) is proven false.

"Double" the N.S.T. axiom.

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

<->

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

from this Tautology we get

~( E(S) A(X) XeS<->phi(X)

<->

~E(S) A(X) XeS<->phi(X) )

which is a restrictive Axiom.

then

~E(r) A(X) Xer<->~XeX

<->

~(rer<->~rer) ***

then

~E(r) A(X) Xer<->~XeX

<->

TRUE

then

~E(r) A(X) Xer<->~XeX

>

> How is "oo" defined in ZFC?

>

|N|

You think there are more than |INFINITE LIST ROWS| Points

between these 2 bars!

---->|------|<-----

Right?

Herc

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