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Re: Matheology § 261
Posted:
May 10, 2013 11:39 PM


On May 11, 1:08 pm, Zeit Geist <tucsond...@me.com> wrote: > On Friday, May 10, 2013 6:28:29 PM UTC7, Graham Cooper wrote: > > On May 11, 10:56 am, Zeit Geist <tucsond...@me.com> wrote: > > > > On Friday, May 10, 2013 4:57:08 PM UTC7, 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 subformula 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  www.BLoCKPROLOG.com



