Re: Cantor's diagonal proof wrong?

From: Tim Peters (tim.one_at_comcast.net)
Date: 11/14/04 

Date: Sun, 14 Nov 2004 05:08:24 -0500

[Curt Welch, with some arguments that depend on the existence of
 integers with non-trivial infinite decimal representations]
...
> Has any one else put forth this same argument

Yup, many times, over many years.

> (or others)

Those too.

> that Cantor's proof is invalid?

If this isn't literally true, it's close enough <wink>: look at sci.math on
any day over the last decade, and you'll find the same basic argument in
some then-current thread.

Rather than repeat all this, how about going to

    http://groups.google.com/groups?group=sci.math

and entering

    Cantor diagonal

in the search box? There are close to 5,000 hits on that today. Broaden
the search to sci.logic and comp.theory to get more. Add words like
"wrong", "idiot", "invalid", "flawed", "refuted", "incorrect", "fallacy",
and "disproof" to get slightly different flavors of confusion.

Of course there's no end to this: simply arrange all the claimed
refutations of Cantor's argument in a list. Make a new refutation whose
i'th word is obtained by picking a random word other than the i'th word of
the i'th refutation in the list. The refutation so constructed will be a
refutation not on the list, and will make about as much mathematical sense
as any refutation on the list.

Now understanding clearly why *that* argument is full of beans is a good
start at understanding why Cantor's argument is not <wink>.

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