> On 16 Dez., 11:02, Rupert <rupertmccal...@yahoo.com> > wrote:
> > Okay, so you seem to be saying that you would take > all the finite > > paths and append an infinite tail to each one, > thereby obtaining a > > countably infinite collection of infinite paths. Is > the claim then > > that this would be equal to the collection of all > infinite paths? Or > > not?- > > It is equal to the collection of all paths that are > defined solely by > their nodes. It is equal to all finite initial > strings of digits that > can be applied in a Cantor-list. (Every digit changed > there has a > finite index.) > > Actually infinite paths like that of 0.010101... = > 1/3 (in binary) > cannot be defined by nodes. > > Regards, WM
So then, WM gives 1/3 as a concrete example of an infinite path of the binary tree which does not belong to the collection of infinite paths of the binary tree. Is it possible that WM will answer the question about the set of all infinite paths of the binary tree which do not belong to the collection of infinite paths of the binary tree, whether this set is finite, countable, or uncountable? If he says that it is uncountable, then what is the whole discussion about?