Re: Cantor's diagonal proof wrong?

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 11/21/04 

Date: Sun, 21 Nov 2004 06:16:42 -0600

On 20 Nov 2004 18:08:27 GMT, curt@kcwc.com (Curt Welch) wrote:

>trimble1@optonline.net (Todd Trimble) wrote:
>> On 20 Nov 2004, Curt Welch wrote:
>> >"*** T. Winter" <***.Winter@cwi.nl> wrote:
>
>> OK, stop right there. You said "the diagonal anti-value can be
>> constructed for any mapping function provided, *which is still a
>> valid idea*. There, you said it: the construction is valid.
>>
>> >But then they make a conclusion that is invalid. They assume that
>> >since the anti-diagonal value being constructed doesn't match any single
>> >row, that it's valid to say that it doesn't match all the rows. And as
>> >valid and as logical as that sounds as that sounds, it's not at all
>> >valid when you are constructing infinite sized real values in a infinite
>> >sized table. This is because it's impossible to construct the entire
>> >anti-diagonal value,
>>
>> Whoa, whoa, whoa. Now you say you can't construct the entire
>> anti-diagonal value. How come the construction was valid only
>> a paragraph ago?
>
>I've already explained this about 10 times. But as long as someone is
>interested, I'll keep going.
>
>The problem is here is 100% language issues. What does "constructed" mean?
>How I was using it has a subtle but very important difference from how you
>were hearing it.

That's correct.

How you're using it also not the same as what it means in the proof
when people talk about constructing that diagonal number - the fact
that your mmeaning for the word is different from what the author
of the proof means by the word is exactly why your currect objections
are irrelevant!

All you're showing is that a _different_ proof, one which looks the
same on the page, but where some of the words are given _different_
meanings, is invalid. That's true, but so what?

>[snipped irrelevant explanations about how no algorithm can
>perform infinitely much computation in finite time.]

************************

David C. Ullrich

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