Re: Cantor's diagonal proof wrong?
From: robert j. kolker (nowhere_at_nowhere.net)
Date: 11/14/04
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Date: Sun, 14 Nov 2004 17:03:07 -0500
Curt Welch wrote:
>
> Lately however, I've come to see things very differently. I now belief the
> proof is totally bogus. And the huge body of work built on top of the
> concept is likewise, totally bogus.
Forget the mysteries of A.I. Show which step in the diagnal proof is wrong.
If a list of decimal expansions cannot be put into 1-1 correspondence
with the integers, neither can the reals in the interval [0,1] which is
the point of the proof. The proof is acheived by showing that a
variation os the n-th digit of the n-th item of the list produces a
decimal expansion equal to a number in [0,1] but which is not on the
list which is a contradiction since we assume the list exhausted all
reals in the interval [0,1]. Why can't this diagonally varied sequence
of digits be in the list? Because it differs from the n-th item on the
list in the n-th place. If it were in the list it would be the K-th item
for some K, but its K-th digit would be unequal to its K-th digit which
is a contradiction.
Show why and where that is wrong.
Bob Kolker
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