Re: Cantor and the binary tree



Virgil wrote:
> 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.

Not that. But your permanently repeated completely unfounded speech
reminds me of Orwell.
> >
> > > > 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.

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

Is here a bijection possible between uncountable sets? Can you
enumerate R <--> R?

Regards, WM

.

Relevant Pages

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