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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