Re: Cantor's diagonal proof wrong?

From: Shmuel (Seymour J.) Metz (spamtrap_at_library.lspace.org.invalid)
Date: 11/22/04 

Date: Mon, 22 Nov 2004 12:05:07 -0500

In <20041120161951.101$VO@newsreader.com>, on 11/20/2004
   at 09:19 PM, curt@kcwc.com (Curt Welch) said:

>Now, what I can show about your diagonal value, is that every
>diagonal you construct is in fact in the table, in row N+1.

No. There is no value of N for which that is true. You are again
confusing a statement about a sequence wits a statement about one of
its subsequences.

>If the table was finite in size, my argument would fall apart.

It fall apart regardless, because you are looking at the wrong
sequence.

>For every row you can show which does not contain the value, I can
>show you another row which does.

No. You can show a row that contains a different, and irrelevant,
value.

>Ok, in the above, I have specified the table first. Or if you want
>to be more exact, instead of starting with "any" set of 1's and 0's,
>let just say the first row is all 0s'. The second row is 1000...
>The third row is 110000... etc.

That table does not contain 11...

>Yes it does. But yet, I can also show that every diagonal number
>which you say is not in the table, is in fact in the table.

The value with all 1s is not in your table.

>In the diagonal proof, we start with an infinite table. But that's
>already a trick of language because infinite tables can't exist.

That's an unwarranted assumption on your part. Further, Mathematics is
not about physical objects, and the Mathematical usage of "exists" is
quite different from the physical usage.

>pretending

That's you, not us.

>by only looking at the first N rows

That's you, not us. The Cantor diagonal argument looks at all rows
concurrently.

>writing ...

That's you, not us. We use universal and existential quantifiers,
functions, etc., to make the meaning precise.

>only valid on finite tables

No.

>And I do not yet know the full nature of those other proofs or the
>full nature of the language they are written in.

Obviously. Yet in spite of not understanding the language, you make
statements about what is valid and what is invalid. If I wrote that
Rodin's "The Thinker" was in the key of G Major, would you not think
that I was a crank? What you have written is fully as egregious. 

-- 
Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action.  I reserve the
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