```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 rationalsI 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 anenumeration 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 formallyHence 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 definedNo, 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 originalenumeration of nodes. You have not, and can not, add all of the paths.>Then you might counter that that is not sensibleOr 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 theright to publicly post or ridicule any abusive E-mail.  Reply todomain Patriot dot net user shmuel+news to contact me.  Do notreply to spamtrap@library.lspace.org
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