Re: Cantor Confusion

In article <1174372833.140688.156790@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

On 19 Mrz., 20:31, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1174292997.710730.80...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

Can we agree upon the following facts?

(1) The infinite paths 0.000... and 0.111... are completely contained
in the complete tree T(oo), i.e., every node belonging to one of these
paths is a node belonging to the tree T(oo).

(2) The set of nodes of the tree T(oo) is countable. In particular,
the number of nodes belonging to one level L(n) is countable for every
n.

(3) There is no node in the tree (including every node of the paths
0.000... and 0.111...) which belongs to a level where uncountably many
paths have been separated or will separate in the next level.

If you agree to these three points, then you may continue your dreams
of whatever you like. I will not further disturb you. And I am sure
every sensible person will share my attitude. If you don't agree,
please state which of the three points is/are wrong in your opinion.

Regards, WM

I fail to see that any of the points WM presents has any relevance
whatsoever to the issue of whether the number of paths in a CIBT is
countable or uncountable.

Does WM agree that EVERY endless sequence of 0's and 1's following that
header of 0 is an infinite path belonging to the tree T(oo)?

If not, which uncountable subset of of those uncountably many endless
sequences does WM argue have been left out?
.

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