Re: Review of Mueckenheims book.

In article <1175944821.407579.166340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

On 2 Apr., 15:02, "*** T. Winter" <***.Win...@xxxxxx> wrote:

Not from set theory, but from graph theory. But you do *not* use the
standard terminology from graph theory. You have some notion about them
that you can not (or want not) to make clear. And every attempt by others
to give set theoretic definitions of your terms is ignored by you, you
rather wish to use your ill-defined terms.

It is clear, to everybody who does not refuse to see it, that there
are not less nodes than separated paths.

I do not know how "separated" paths differ from ordinary paths in a
complete infinite binary tree, but it is a theorem ( has been proved) in
ZF and NBG that there are more ordinary paths than nodes in such
infinite trees, and mathematicians do not reject theorems.



Concerning your position, you
could also claim that in the *infinite* sequence 21212..., there are
more 2's than 1's (or the other way round). That would make as much
sense as the claim that there are more separated paths than nodes in
the tree.

AS we have no clear explanation from WM as to how his "separated" paths
might differ from ordinary paths, no one is claiming what he claims they
are claiming.

Mathematicians only see that it is a theorem in ZF and NBG, and various
other set theories, that in any complete infinite binary tree there are
more ordinary paths than nodes.
.

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