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. This list is only written in a somewhat unconventional form.