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Re: Who's up for a friendly round of debating CANTORS PROOF?
Posted:
Aug 19, 2011 1:47 PM
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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.
------------------
Cantor's proof similarly fails at other levels of analysis aswell,
when moving from a finite analysis to the infinite case.
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!
This is in error! It works on a case by case basis examining one anti-
diagonal at a time, but due to INFINITELY MANY PERMUTATIONS the
possible diagonals are saturated with every possible digit sequence up
to infinite length of the expansion, depending on the ordering of the
list not the list itself.
Nobody is sci.math will acknowledge that the ordering of the LIST,
when determining the missing real, is a FREE VARIABLE!
AD = digitrotate ( sDIAG ( SET, p ))
p is a FREE VARIABLE in AD!
sDIAG is a 2 parameter version of DIAG ( LIST )
where p specifies which permutation of the SET of reals to use.
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ANALOGY: sci.math think they have an unbreakable lock using an
infinitely long password! They even allow us to use infinitely many
infinitely long passwords! (*from infinitely many permutations of the
list to choose from*) How long would that take to crack with infinite
attempts at once?? haha
Herc
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