SPQR
Posts:
411
Registered:
8/12/11
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Re: Who's up for a friendly round of debating CANTORS PROOF?
Posted:
Aug 19, 2011 4:42 PM
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In article
<1aec7ee6-eeca-4080-9ac0-daaca285b75c@c8g2000prn.googlegroups.com>,
Graham Cooper <grahamcooper7@gmail.com> wrote:
> On Aug 20, 5:55 am, SPQR <S...@roman.gov> wrote:
> > In article
> > <6b943b1d-b8ac-4991-91a7-5cb916703...@d8g2000prf.googlegroups.com>,
> > Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
> > > On Aug 20, 2:46 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > or this one: The limit, i.e., the complete Cantor-list contains every
> > > > real number including its anti-diagonal whereas every finite initial
> > > > segment of the Cantor list contains only a finite number of reals
> > > > excluding its anti-diagonal.
> >
> > > > Regards, WM
> >
> > > Yes effectively correct!
> >
> > > In the infinite LIST analysis, every digit of the anti-diagonal
> > > appears one after the other to infinity! FACT!
> >
> > > All_digits_of_the_antiDiagonal_appear in the LIST OF REALS in order,
> > > from digit_1 onwards left to right!
> >
> > > In this trivial finite version.
> >
> > > LIST
> > > 0.123
> > > 0.456
> > > 0.789
> >
> > > DIAGONAL = 0.159
> > > ANTI-DIAGONAL = 0.260
> >
> > > The diagonal sequence 0.260 is indeed missing!
> >
> > > This is nothing at all to do with an infinite LIST!
> >
> > > 0.260 is indeed present in any rudimentary expressive infinite LIST of
> > > REALS!
> >
> > > Anti-diagonalising clearly fails to generate a unique sequence of
> > > digits! Cantor followers shift their argument at this point with a
> > > myriad of segregated supporting arguments.
> >
> > That is partly because "herc" is not dealing with Cantor's own theorem
> > but with a derived and inferior version of it.
> >
> > Cantor's original theorem was about functions from |N to the set {w,m}
> > Cantor said that for any given infinite list, say indexed by the
> > positive integers, of such function, there were other such functions
> > ommitted.
> > And it is easy to see that the unique function from N to {w,m} which
> > differed from the n-th listed function at n cannot be in the list.
> >
> >
> >
> > > ------------------
> >
> > > Cantor's proof similarly fails
> >
> > Nonsense. Find where the obove original argument fails?
> >
> > > Using a FINITE LIST like the example above, it's clear that no matter
> > > which permutation of the LIST is used, the DIFFERENT ANTI-DIAGONAL
> > > from the SAME SET OF REALS is also missing from the LIST!
> >
> > > Cantor followers use this methodology to *incorrectly* conclude that
> > > since ANY PERMUTATION of a finite list Cantor's proof succeeds, so
> > > then ANY PERMUTATION OF THE INFINITE LIST CANTORS PROOF SHOULD
> > > SUCCEED!
> >
> > Nope! since the Cantor method makes no assumptions about the nature
> > of the list, other then its being a countably infinite list, the
> > method applies correctly to ANY such list.
> Exactly!
The proof applies correctly to any such countably infinite list.
You have not refuted that and cannot refute it, because it is trivially
true.
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