Re: Two results of set geometry

In article <1190035747.850345.62360@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueckenh@xxxxxxxxxxxxxxxxx> writes:
On 17 Sep., 02:57, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1189945589.699206.305...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueck...@xxxxxxxxxxxxxxxxx> writes:
...
> My claim is the existence of the bijection.

By showing an injection from nodes to paths. But that one is trivial. For
a bijection you also need an injection from paths to nodes, or prove that
your injection is also a surjection. Your injection is not a surjection,
because there is no node that maps on the path 0.10101010..., so you have
either to show an injection that is also a bijection or an injection from
paths to nodes.

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.

then it is the supremum
of the path leading to it (compare the triangular matrix and the
missing row 111... which exist only as supremum, not taken). The
number of paths, however, is countable. This implies the countability
of he nunmber of suprema.

This is nonsense. I ask you to show that it is a surjection but you do
not do so. You provide some nonsense. Again, in *what* way is your
injection also a surjection.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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