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 01:41:39 -0500

In <20041120010444.873$AF@newsreader.com>, on 11/20/2004
   at 06:04 AM, curt@kcwc.com (Curt Welch) said:

>It's kind of funny that I come here and start a debate on Cantor's
>diagonal proof only to find out it's a very common debate that new
>guys keep bringing up time and time again and all the old timers are
>sick of it.

It didn't start with Cantor. The generic category is "circle
squarers".

>The idea is that only the description of the processes exists.

There is no process to describe.

>That is what we manipulate when we talk about infinite sets.

No. That's your basic fallacy.

>My "attack" is really a search for understanding

No. You are starting with some incorrect obsessions, and you will not
achieve understanding until you abandon them. You are, in fact,
actively evading understanding.

>What would be the value of looking into this? Well, if the current
>practice allows for exploring abstractions that can't apply to this
>universe,

ObWigner Those who have attempted to do so, e.g., G. H. Hardy, have
failed. Physicists and others keep finding uses for pure Mathematics.

>it might be interesting if we could figure out how to put up a fence
>to make it clear what work was inside the fence, and what work was
>exploring abstractions outside the fence. I believe most of
>mathematics would still be inside the fence.

I doubt it. More likely the fence would be in the wrong place and you
would cut off work that would ultimately have had practical
application. It's very difficult to predict the unexpected accurately
and precisely. 

-- 
Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action.  I reserve the
right to publicly post or ridicule any abusive E-mail.  Reply to
domain Patriot dot net user shmuel+news to contact me.  Do not
reply to spamtrap@library.lspace.org
Quantcast