```Date: Jan 13, 2013 3:56 PM
Author: Virgil
Subject: Re: Matheology � 191

In article <3c651dfd-5d3d-4464-bb03-fea1c590207b@10g2000yqk.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 13 Jan., 13:15, Zuhair <zaljo...@gmail.com> wrote:> > > What mean nothing more than saying that we have Countably many FINITE> > paths> > Yes, and it is not intuitive nor needs it any formalization to> recognize that everything that happens in Cantor-lists happens withing> finite paths (or sequences of digits). It is absoluteley impossible> that something happens elsewhere! And if a list contains all possible> finite paths (which is possible as they are countable) then Cantor's> "proof" proves the uncountability of a countable set.Not unless the anti-diagonal is finite, which it can't be, since those finite "paths" being listed do not, and can not, have a finite upper bound on their lengths, so there cannot be an finite upper bound on the anti-diagonal's length.The obvious flaw in WM's argument shows how poorly he grasps what is really going on.> > Note again: everything that happens in a Cantor-list happens withing> finite paths or finite initial segments of the anti-diagonal.But there is still no finite upper bound on the segments of the anti-diagonal required. Thus even with all finite entries to the list its anti-diagonal must be infinite.> > And please do me a favour and stop parroting of uncountable sets> unless you can explain how something can happen *after* all finite> initial segments. I will continue to speak of uncountable sets until you can show that the set of all infinite binary sequences ( or functions from |N to {01}) can be listed with no anti-diagonal missing.And as you cannot do this, you lose!--
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