Virgil
Posts:
8,833
Registered:
1/6/11


Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 30, 2012 3:18 PM


On 12/29/2012 11:22 AM, WM wrote: > On 28 Dez., 23:04, Virgil <vir...@ligriv.com> wrote: >> In article >> <2925a2eac16d483e91da3bb0084e7...@b16g2000vbh.googlegroups.com>, >> >> WM <mueck...@rz.fhaugsburg.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. > > Definitions need not be proven. That they are instantiated must be proven, and that you have not done.
You have not proven that there is a CIBT constructed or constructible so as NOT to contain uncountably many paths, whereas many have proven that any CIBT must have more than any countable set of paths in order to be a COMPLETE INFINITE BINARY TREE.
Given any countable set of such paths, any proof that they are countable requires that they be listable, but one can prove that they are not listable by showing that no list of them can be complete. And no mater how vociferously WM tries to argue otherwise, in standard mathematics that can all be done. 

