Re: Cantor's diagonal proof wrong?

From: Curt Welch (curt_at_kcwc.com)
Date: 11/14/04 

Date: 14 Nov 2004 19:05:04 GMT

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?

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. 

-- 
Curt Welch                                            http://CurtWelch.Com/
curt@kcwc.com                                        http://NewsReader.Com/

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