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Re: another boring critisism of Cantor's Theorem
Posted:
Mar 30, 2004 5:26 AM
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=?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= <jcsantos@fc.up.pt> writes:
>Craig Feinstein wrote:
> > Here is another question: I look on the web and find a ton of papers
> > trying to refute Cantor's Theorem. (Just Google "Cantor diagonal
> > wrong" and see what you get.) I have never seen one of them that
> > convinced me. Why is there so much opposition to this theorem when
> > most other famous theorems are pretty much universally believed?
>There's a slight confusion here. One thing is Cantor's theorem stating
>that the reals are uncountable and another thing is Cantor's diagonal
>argument, which was actually Cantor's second proof of his theorem; see
>http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof
>or the article "Georg Cantor and transcendental numbers" by Robert Gray
>(American Mathematical Monthly 101, No.9, 819-832 (1994)).
>What I fail to understand is this: why is it that those who attack
>Cantor's diagonal argument do not attack also is other proof of his
>theorem?
I would suggest that either they do not know about it, or they do not
understand it. The one person whom I have seen arguing about it on
sci.math did not understand it.
David
"But I'm always true to you, darlin', in my fashion,
Yes, I'm always true to you, darlin', in my way."
-- Lois Lane
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