Virgil
Posts:
9,012
Registered:
1/6/11


Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 3:14 PM


In article <96a45cc2099b4ebc93ac05754442f6b1@a8g2000vby.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 26 Dez., 10:12, Virgil <vir...@ligriv.com> wrote: > > > > Try to find and > > > identify by nodes only one further path. > > > > AS soon as you tell us what paths you have included in your tree, > > So you do no longer claim that the Cantorargument works by digits or > nodes?
As usual, you draw unwarranted conclusions from everything.
As one identifies a path as a particular set of digits or nodes, how is asking you to identify your paths in any way overlooking them? > > > we > > will be able to tell you at least some of the ones that you have left > > out. But until you show us your paths we have no way of knowing which > > ones are yours and which ones are not yours. > > Although I told you all the nodes of my paths (namely all nodes of the > Binary Tree) and no nodes of your paths (namely the empty set of > nodes), you cannot distinguish my paths and your paths.
A path being a set of nodes, to distinguish it from other path one must specify at least infinitely many of its nodes as being particular to that path before it can b separated from any other path, but you never have done this with any of your paths, so there is no telling which paths you have.
You have also not proved that your set of paths is countable, which can only be done by proving that they can be listed, and most easily done by providing such a list.
> But according > to Cantor's argument, you should be able to distinguish the diagonal > by nodes only.
Only if one has a list of all the paths one wishes to distinguish it from.
Since you claim that you set of paths can b isted, lets see you actually do it. > > > > Then your claim may be > > > considered by rational and sober thinkers. > > > > It already has been considered by rational and sober thinkers > > like you > > > and > > accepted by them and it is only drunk 'tinkers' like yourself who object. > > Object to what? To your claim that you have a countable set of paths (in the form of infinite binary sequences) which includes every possible innfinite binary sequnce.
To prove your set is countable you must prove it to be listable, since that is the same thing, but any listing of such infinite binary sequences is provably incomplete, a fact know to all here but denied by WM. 

