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?