Re: Cantor Confusion

In article <1174137052.814421.258150@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

On 16 Mrz., 15:54, Carsten Schultz <cars...@xxxxxxxxx> wrote:
mueck...@xxxxxxxxxxxxxxxxx schrieb:


Don't mistake the infinite number of finite paths with infinite paths.

I don't.

I am not sure. A set of finite paths is bounded by aleph_0.

Aleph_0 cannot be a bound on an ordered set of paths, or even on a
partially ordered set of pahts, unless it is itself a path.

Some sets of finite paths are not bounded at all.

In the union of all finite trees every path has a finite length, given
by a natural number of nodes. Presently we are considering the union
of all such finite paths. (The union of all finite natural numbers is
an infinite union - nevertheless this union cotains only finite
numberrs.)

The set of all finite subsets of N is countable, the set of all subsets
of N is not,

Alas, these subsets, as represented by indexes of paths, cannot be
distinguished.

They are not represented by "indexes of paths" but are, for each path,
the sets of levels at which it has left branchings.

As such as sets for different paths must be different, and different
sets produce different paths, we have the set of paths bijecting with
P(N).



The set of all finite paths is identical with the set
of all finite and infinite paths.

How can that be when one set contains members the other lacks?


As long as the paths exist as sets of nodes within the tree, they are
countable.

Since the set of all subsets of the set of all nodes is uncountable, and
paths 'are' such subsets, WM has much yet to prove and no talent for
proving.




After having left the tree and lost any contact to nodes,
the paths do no longer represent real numbers. And this will not
change, regardless of the number of opposing believers.

As it is pure nonsense, no one but WM believes it.

We, who do not accept WM's unproven claims as gospel, do not need to
have any path separated from its tree or its nodes in order to find WM's
errors.
.

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