Re: Cantor Confusion

In article <1175178657.434003.303550@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
On 29 Mrz., 04:23, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
> > It still says *nothing* about the number of single paths.
>
> An uncountable number of paths existing separated from each other
> would form a level with uncountable man nodes.

Pray, for once, show a *proof* of this statement.

It is a result of set theorey that uncountably many is greater than
counatbly many. If you have a greater set, then there must be more
elements than in a smaller set. If n elements exist in a set, then
they must exist simultaneously. That means there must be some domain
where this happens.

Yes. The domain is the set of paths. But you state there must be a *level*
where it happens. Pray show a for once a *proof* of that statement.

> But we know that there
> cannot be such a level, including all infinity of the complete tree.

Indeed, there is not. Nevertheless there are uncountably many infinite
paths.

That is obviously wrong. The necessity of as much separation points as
separated paths is not restricted to the finite tree. It is required
in any case. Otherwise there must be paths with no connection to the
root node. But those constructs are not paths.

Show a *proof* of that necessity for infinite trees.

You do not believe it, but you fail to prove it. It is just your
insistence that if all paths do separate from each other that there must
be a level where all paths are separated from each other.

In particular, there must be all separation points in the tree.

You say: There are all uncountably many separated paths in the tree.
But there are not all uncountably many points of separation in the
tree.

Right. And that is provable.

Obviously bad logic. But you say, it is good logic. So let it be.
Antilogic cannot be disproved by logic.

You are indeed not able to disprove it. Simply because you do not
understand the logic.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.