Re: Cantor and the binary tree

In article <MPG.1cffa39924382800989d30@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
>
> > So WM is wrong yet again.
> >
> > And TO too!
> >
> Virgil, you have repeated this nonsense now six or so times verbatim. If you
> were paying attention, I think you'd realize this is not related to what WM
> is
> claiming. Look at my argument concerning insertion of a node, and respond to
> that. It's the relative number of paths vs. nodes that WM is addressing, in
> response to your claims that you have an infinite tree with uncountable paths
> (because you're hung up on leaf nodes for some reason) and countable nodes,
> when paths are always less numerous than nodes. Pay attention. It's no wonder
> these discussions with you go around in circles, when you don't even know
> what
> they're about.

Each node in a maximal binary tree is the end node of a finite path from
the root node, but no node is the end node of an infinite path from the
root node,

So that any assumption that the number of nodes equals the number of
unending paths requires proofs that neither WM nor TO have produced, or
can produce.

I can produce a bijection between the number of nodes in such a tree and
N, and I can produce a bijectin between the number of unending paths and
P(N).
.

Relevant Pages

  • Re: Cantor and the binary tree
    ... >> Virgil, you have repeated this nonsense now six or so times verbatim. ... >> response to your claims that you have an infinite tree with uncountable paths ... > I can produce a bijection between the number of nodes in such a tree and ... and I can produce a bijectin between the number of unending paths and ...
    (sci.math)
  • Re: infinity
    ... >> Virgil wrote: ... Order is irrelevant to the bijection, ... >>> bijection is based on the ordering of members of the sets being bijected. ... >> series would equal to the cardinality of N. ...
    (sci.math)
  • Re: Two results of set geometry
    ... I ask for an injection from paths to nodes, ... > I gave a bijection between all infinitely many paths and all ... The correct SEQUENCE of digits for EVERY path remains to be mapped, ... I care for you, Virgil. ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... Virgil wrote: ... There are no finite paths in my tree. ... For that sake enough zeros are in the ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... Virgil wrote: ... >> Randy Poe wrote: ... >>> If Mueck actually tried to read and follow my example, ... >> You may try to construct any bijection. ...
    (sci.math)
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