SPQR
Posts:
411
Registered:
8/12/11


Re: Who's up for a friendly round of debating CANTORS PROOF?
Posted:
Aug 19, 2011 4:42 PM


In article <1aec7ee6eeca40809ac0daaca285b75c@c8g2000prn.googlegroups.com>, Graham Cooper <grahamcooper7@gmail.com> wrote:
> On Aug 20, 5:55 am, SPQR <S...@roman.gov> wrote: > > In article > > <6b943b1db8ac499191a75cb916703...@d8g2000prf.googlegroups.com>, > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > On Aug 20, 2:46 am, WM <mueck...@rz.fhaugsburg.de> wrote: > > > > > > or this one: The limit, i.e., the complete Cantorlist contains every > > > > real number including its antidiagonal whereas every finite initial > > > > segment of the Cantor list contains only a finite number of reals > > > > excluding its antidiagonal. > > > > > > Regards, WM > > > > > Yes effectively correct! > > > > > In the infinite LIST analysis, every digit of the antidiagonal > > > 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 > > > ANTIDIAGONAL = 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! > > > > > Antidiagonalising 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 nth 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 ANTIDIAGONAL > > > 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.

