Re: Cantor and the binary tree

mueckenh@xxxxxxxxxxxxxxxxx wrote:

of paths always equals that of the nodes + 1. It is simply impossible
to assume that one of these numbers becomes uncountably infinite while
the other remains countably infinite.


Wrong. 2^(aleph_0) > aleph_0.

List all the infinite binary sequences with a bijection to the integers. Now flip the n-th digit of the n-th sequence in the list. This cannot occur anywhere in the list. Contradiction. Such a bijection to the integers does not exist.

Bob Kolker
.

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