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Re: Cantor Confusion

Subject: Re: Cantor Confusion
From:
Date: 30 Sep 2006 05:40:19 -0700
Newsgroups: sci.math
Virgil schrieb:

> In article <451dddd9@xxxxxxxxxxxxxxxxxxx>,
>  Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
>
>
> > >
> >
> >  The original proof was regarding a complete language using
> > at least two symbols, m and w, no?
>
> Not quite. Two disjoint sets of synbols.
>
> > That was later conflated to a proof about the reals.
>
> It was later shown that it could be modified to form a proof that the
> set of all reals is uncountable.

This was *not* "later shown", but at the very time of publishing in
1890/91 Cantor considered this very proof as the proof of the
uncountability of he reals.

Cantor, in the first paragraph: " Es läßt sich aber von jenem Satze
[uncountability of the reals] ein viel einfacherer Beweis liefern, der
unabhängig von der Betrachtung der Irrationalzahlen ist."
My translation: "Here is a much simpler proof of the theorem
[uncountability of the reals] which is independent of the reference to
irrational numbers"

Regards, WM


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