Re: Cantor and the binary tree

Robert Kolker wrote:

> 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.

"becomes"? Muck's fuzzy metaphors are sabotaging him again.
The fact is that the nodes in this tree form a countable
set and the paths form an uncountable set. "becoming"
has nowt to do with that.

>
> 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.

One can hardly imagine a simpler mathematical proof. Alas, it's still
beyond the limits of Muck's feeble intellect :-(

--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Elegance is an algorithm"
Iain M. Banks, _The Algebraist_
.

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