Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 28, 2012 5:04 PM
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In article
<2925a2ea-c16d-483e-91da-3bb0084e7505@b16g2000vbh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 27 Dez., 21:49, Virgil <vir...@ligriv.com> wrote:
>
> > > It is the set
> > > of all finite paths extending from the root node to a given node.
> >
> > In every Complete Infinite Binary Tree, every finite path ends at the
> > root node of of another Complete Infinite Binary Tree. So for every
> > finite path, there are uncountably many extensions of it in every
> > Complete Infinite Binary Tree.
>
> And every extension is contained in the CIBT constructed from all
> finite paths.
Claimed but never proven.
And only true if one is allowed to chain finite paths from an infinite
set of finite paths like one chains nodes from the infinite set of
nodes, into chains of infinitely many finite paths.
>
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