Re: Cantor and the binary tree

In article <1118242728.867905.19880@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Virgil wrote:
>
> >
> > In a maximal binary tree, each maximal path passes through, and thus
> > determines, an infinite set of nodes. There are uncountably many such
> > infinite sets of nodes.
>
> Your permanence reminds me of Animal Farm. Did you read Orwell? "Four
> legs good, two legs bad." (But later that was changed.)

When WM has no valid mathematical arguments leftt he imagines that
non-mathematical arguments will impress.
>
> > > Double the number of nodes.
> >
> > "Doubling" an infinite set has no effect on its cardinality.
>
> Therefore we can do that. Map a node on every path coming out of it.
> Map a node on every child path of them and continue. Then every path
> carries 1 + 1/2 + 1/4 + ...1/2^n nodes. For n --> oo every path
> carries two nodes. There are only bits which can be enumerated by
> finite naural numbers. And for every finite natural number induction is
> valid. Therefore, every path carries two nodes. ==> The set of paths is
> countable.

Which two nodes does the path of all left branches "carry"

Which tow nodes does the path of alternating left and righ branches
"carry".

Give a specific algorithm for finding the path given the two nodes that
it "carries", or vice versa, an algorithm for finding the two nodes from
the path.

Absent these algorithms, the alleged correspondence is no more than a
smoke dream.
.

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