In article <faaecaf1-57f9-435a-aba9-f731cde7f5da@a36g2000yqc.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 16 Jun., 23:44, Virgil <virg...@nowhere.com> wrote: > > > > The tree is constructed by all terminating paths with tails 000... > > > > Which is a countable set of paths, and therefore, by Cantor, does not > > include all paths. > > By Jove, it does! > > > > > same tree could be constructed by all terminating paths with tails > > > 0.010101... > > > There is no difference. > > > > Any set of paths, or other sets of nodes, whose union contains as > > members all nodes of a prospective maximal infinite binary tree tree can > > be used to construct that tree, whether that set of sets of nodes > > contains as members all the paths of that tree or not. > > > > Once one has the set of all its nodes, regardless of how they are come > > by, one has the tree, and all its paths derive from the node set and tha > > 'parent of' relation, not from any a priori set of paths. > > Once one has the set of all binary sequences one has a list that > contains all real numbers.
Wrong! One has a set which cannot be made into a list, as Cantor proved.
> This list is only written in a somewhat > unconventional form.
An incoherent form, since it cannot be written as a list at all. > > Regards, WM
