```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 WFFwith the property  phi v ~phiA WFF with the Stipulation  phi XOR ~phiN.S.T. works fine!  (a variation thereof)The CONTRADICTIONrer <-> ~(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<->TRUEthen~E(r) A(X) Xer<->~XeX>> How is "oo" defined in ZFC?>|N|You think there are more than |INFINITE LIST ROWS| Pointsbetween these 2 bars!---->|------|<-----Right?Herc--www.BLoCKPROLOG.com
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