Re: Two results of set geometry

In article <1190632327.357863.49790@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueckenh@xxxxxxxxxxxxxxxxx> writes:
On 20 Sep., 04:39, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1190035747.850345.62...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueck...@xxxxxxxxxxxxxxxxx> writes:
....
> Every "index" of 0.101010... and every initial segment of 0.101010...
> is in the bijection.

*finite initial segment*.

> So what is missing?

The complete path. Which node maps to the complete path?

> But even if you claim that
> 0.101010... does exist "in some other form",

I do not claim anything like that at all. I only claim that your
mapping does not map a node to that path, so that your mapping is not
a surjection.

My mapping maps includes every node of every paths.

Yup. Because it is a mapping from the set of nodes to the set of paths.

Therefore it
includes every initial segments of every path - except such which do
not consist of nodes.

Makes no sense. There are no initial segments of paths in the domain
of the mapping nor in the range, so what do you *mean*?

Do you think that 0.101010... consists of more
than of the complete set of its initial segments?

Irrelevant. You gave a mapping from the nodes to the paths, you have to
show that in the range of that mapping each path is present, you have not
done so.

> The
> number of paths, however, is countable. This implies the countability
> of he number of suprema.

This is nonsense. I ask you to show that it is a surjection but you do
not do so.

There is a bijection between all really existing paths and N.

Again, *what are really existing paths*? Why do you continuously invent
new terminology without explanation.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.