Re: Cantor and the binary tree

On 20 Jun 2005 04:09:53 -0700, mueckenh@xxxxxxxxxxxxxxxxx wrote:
>> This no more proves countability of the set of paths than the fact that
>> lists of bits can represent all reals in [0,1] proves the reals
>> couontable. The set of all such lists, like the set of all those maximal
>> paths, is uncountable.
>
>By construction of the tree we see that all binary representations
>which differ at a finite position are represented by bunches (=
>non-empty subsets) of paths in the tree. Further we see that they can
>distinguish themselves only at nodes or branches. The occasions to do
>so are countable.

What is it you are smoking? Can I have some? Even in finite binary
trees, the number of paths is greater than the number of nodes where
branching occurs.

Martin

.

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