Re: Request for Peer Review - Refutation of Cantor Theorem Conclusion

On 27 Apr 2006 10:50:58 -0700, "Scott" <ToaTerra@xxxxxxxxx> wrote:

I would therefore suggest that you
first try to identify a flaw in the proof of Cantor's Theorem.

Agreed. That is my first set of proofs. Cantor's proof itself
(specifically the diagonal argument) is solid (as far as I can tell). I
propose an alternate interpretation of the conclusion. Cantor's Theorem
states that a mapping function f does not have the diagonal set D in
its image. I propose Cantor's proof also shows D is not an element of
the powerset; thus f is preserved as a bijection. At this point, my
knowledge fails me and I need an expert to drill down and make sure
there are no hidden gotchas.

There are no _hidden_ problems here. The problem is right
there in plain sight: That set D _is_ an element of the
power set. You can "propose" that it's not all you like,
doesn't change the fact that it is.

To be more careful: Assuming the standard axioms of set
theory, D _is_ an element of the powerset and hence
your proof is simply wrong. If you have some other
collection of axioms for set theory in mind you need to
start by saying exactly what the axioms are.

If you succeed, you will be quite
famous and will have no trouble at all finding volunteers to review your
work.

lol. Isn't this a circular logic argument? Famous -> volunteers and
volunteers -> famous ;-)


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David C. Ullrich
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