Re: Cantor Confusion

On 16 Mrz., 21:31, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1174055000.972069.261...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

The function of all cross sections, f: n |--> 2^n, is "continuous" in
the sense that never a jump by more than a factor 2 can occur because
the nodes of the tree are connected by an untearable network. The
domain is the same as the range, namely N. That is fact, not by claim
but by construction of the tree. That's why I constructed it.

You constructed the tree to show that 2^{n+1} <= 2*2^n ? Well, that
really must have been fun. Ok, I agree on this. Now we know a property
of the function

f : N -> N
n |-> 2^n.

This does not tell us anything about 2^aleph_0.

aleph_0 is not a natural number.

Are you just discovering that?

Every index of a digit of a real number or of a node, however, is a
natural number. Therefore it is of no interest at all to speculate
about what happens "at aleph_0". That should you try to discover.

Regards, WM

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