Re: Cantor's diagonal proof wrong?

From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 11/14/04 

Date: Sun, 14 Nov 2004 14:13:43 -0700

In article <20041114140504.885$0X@newsreader.com>,
 curt@kcwc.com (Curt Welch) wrote:

> Torkel Franzen <torkel@sm.luth.se> wrote:
> > curt@kcwc.com (Curt Welch) writes:
> >
> > > How can you show my
> > > argument is invalid and at the same time, keep Cantor's logic about the
> > > relationship between the integers and reals as valid?
> >
> > If you're a genuine crank, it is of course quite impossible to show
> > you anything. If you're not, you'll find out about these things for
> > yourself.
>
> So far, everyone has taken issue with my defintion of "reals" or with the
> idea that my mapping from reals to integers is not complete. And that's
> fine. It is not easy for me to argue my position there because I don't
> have the correct foundation.
>
> But how can you show me (ok, a student of your's who is not a crank), where
> the flaw is in the logic I used to show that the table of integers does not
> contain all the integers?

The "contradiction" is that you cannot prove that *every* table of
integers is missing some integers whereas Cantor has proved that *every*
table of reals is missing some reals (in fact missing more than are
actually tabulated).
>
> It's clear from the defintion of the table, that it does contain all the
> integers. Yet, when we apply the same logic which Cantor's proof used, we
> are able to contruct an integer which is not in the table.
>
> Is your position that the integer we construct is not an integer? So
> therefor it's not surprising that it is missing from the table?
>
> Ah, I think that argument would fit into the arguments I've seen put forth
> in this thead so far. If that is the position, then I see I won't be able
> to stop here. I'll have to go deeper. I'll have to find a way to show the
> contradiction exists in some set of axioms. Damn.

Relevant Pages

  • Re: Cantors diagonal proof wrong?
    ... curt@kcwc.com (Curt Welch) writes: ... > argument is invalid and at the same time, ... > relationship between the integers and reals as valid? ... If you're a genuine crank, it is of course quite impossible to show ...
    (sci.math)
  • Re: i still havent get it
    ... > The method does not give us real numberthat are missing from any list. ... The modified Cantor precedure applied ... Mathematical claims (like the claim that there is no list of all reals) ... axiom anything provable from other axioms. ...
    (sci.math)
  • Re: Cantors "proof"
    ... Keckman wrote: ... Where there are more numbers missing than there are listed. ... As long as each list of reals is countable (an image of ... in one of the usual ways to avoid the dual representation problem ...
    (sci.math)
  • Re: Attempts to Refute Cantors Uncountability Proof?
    ... For the simple reason that Cantor's proof assumes that the starting ... countable list of all the reals. ... insertion method not indicate there are always more rational numbers? ... value is always missing from the list. ...
    (sci.math)
  • Re: Characterization of an Open Set in the Reals
    ... definition is intimately tied to the reals. ... And your missing-point proof shows convex iff connected. ... suppose we take intervals of the rationals. ... claim something was missing. ...
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