Date: May 16, 2012 5:07 PM
Author: Shmuel (Seymour J.) Metz
Subject: Re: On the diagonal argument again

In <jouvko$58d$1@speranza.aioe.org>, on 05/16/2012
   at 02:24 AM, "LudovicoVan" <julio@diegidio.name> said:

>You can't.

Nor can anybody else.

>You might say that I only enumerate the rationals

I might, if you enumerated all of the rationals, which you didn't.

>(I must take it that you have partly misspoken)

No.

>although you provide no support.

If you didn't understand it when other posters explained it to you,
why would I want to make another futile attempt?

>Nor you have solved the little puzzle below,

What puzzle?

>No what?

No, logic doesn't tell you that an enumeration of the nodes is an
enumeration of the paths. In fact, logic tells you that it isn't.

>I actually have,

No, you have neither defined "limit" nor proven any properties for
"limit".

>although not formally

Hence it's just hand waving.

>think inductive definitions,

You haven't given one.

>think the definition of the limit case.

You haven't given one.

>Here the sequence is inductively defined

No, a *different* sequence is inductively defined.

>and the limit is defined (by me) to be the diagonal and the
>anti-diagonal sequences. 

With that definition you have only added two paths to your original
enumeration of nodes. You have not, and can not, add all of the paths.

>Then you might counter that that is not sensible

Or I might not. Actually, it is sensible but not particularly useful.

>Anyway, how I have (informally) 
>justified that limit belongs to what you have snipped,

But not that adding the limits gives you an enumeration of all paths.

-- 
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