Re: Cantor Confusion

In article <1173954799.919385.61730@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
On 13 Mrz., 14:15, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1173724460.248046.46...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueck...@xxxxxxxxxxxxxxxxx writes:

Terminating paths.

*Passing* path-bundles.

Those are *terminating* paths. (A path-bundle can be seen as a terminating
path: it is a set of nodes containing a finite number of nodes.)

A path bundle splits off into two bundles which pass said node.
Therefore every set of path-bundles in the tree has a finite cardinal
number

As long as path-bundles are finite sets of nodes that is right.

This, in the "limit", may yield an infinite number, but certainly not
an uncountable number without having an intermediate countably
infinite number.

I do not know. What do you understand under "limit"?

The tree is continuous because its nodes are connected by paths. There
is never more than the factor 2. There are no interruptions possible
and no jumps from "finite" to "uncountable". Your claim would require
that.

My claim requires nothing of the sort. The number of finite paths is
countable. The number of infinite paths is uncountable. There is no
jump from countable to uncountable, there is a jump from finite paths
to infinite paths.

PS: What about the review of chapter 10?

I have not had much time, but I am working on it.
--
*** 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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