Re: Cantor Confusion

On 16 Mrz., 21:06, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1174042350.684943.146...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





mueck...@xxxxxxxxxxxxxxxxx wrote:
On 16 Mrz., 01:31, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1173954799.919385.61...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

For even binary trees ( where even here means all paths are of equal
length),

Only those are under discussion here.

the number of paths increases exponentially with number of
levels (lengths of a path). Adding 1 to the number of levels doubles the
number of paths.

The tree is continuous because its nodes are connected by paths.

That is a distinctly non-standard meaning for "continuous" in
mathematics.

It shows, however, that the number of paths cannot jump from finite to
uncountable.

It shown no such thing.
If n can jump from finite to aleph_0, then 2^n can jump to 2^aleph_0.

Not if the function is continuous as is the number of paths-bundles in
the tree. Between uncountable and finite, there is mor than a factor
of two.

Regards, WM

.

Quantcast