Date: Dec 9, 2012 3:19 PM
Author: Zaljohar@gmail.com
Subject: Re: Mathematics in brief
On Dec 9, 10:59 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 9 Dez., 20:37, Zuhair <zaljo...@gmail.com> wrote:

>

> > > Only a countable subset can be represented by the Binary Tree. The

> > > reason is that no path is really actually infinite.

>

> > Then you are not addressing what Cantor was speaking about, he is

> > speaking about reals represented by ACTUALLY infinite sequences (paths

> > in your case). It is clear that the set of all reals represented by

> > FINITE sequences is countable, but those are just a very small subset

> > of the set of all reals.

>

> > If one assumes Actual infinity, then it is easy to recover the

> > diagonal path from any bijection between the reals and the set of all

> > paths of the infinite binary tree, and this will be a path that is not

> > present in the tree of course.

>

> Then you are wrong from the scratch. Every real number has a

> representation by an infinite sequence (= infinite path of nodes in

> the tree). But as my proff shows I construct the whole Binary Tree by

> countably many paths. There are not more nodes available to add

> further paths.

>

> >You will need uncountably many infinite

> > binary trees to recover all the reals.

>

> That is purest nonsense. And it has nothing to do with Cantor's

> diagonal which is of course an infinite sequence of digits

> corresponding to a path in the Binary Tree.

>

Yes corresponding to an ACTUAL infinite path in the Binary Tree, which

is something that you already refuse to address.

Zuhair