Re: Cantor Confusion

mueckenh@xxxxxxxxxxxxxxxxx schrieb:
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.

Using a word does not constitute proof.

And indeed sup_{n<aleph_0} 2^n = aleph_0 < 2^aleph_0,
so in this sense the function kappa |-> 2^kappa is not continuous. If
you can prove (not claim!) by using your tree that it is, then you will
finally have succeeded in showing that ZF is inconsistent.

Have fun,

Carsten

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Carsten Schultz (2:38, 33:47)
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