On 17 Jun., 21:37, Owen Jacobson <angrybald...@gmail.com> wrote: > On 2009-06-17 14:55:38 -0400, WM <mueck...@rz.fh-augsburg.de> said: > > > On 17 Jun., 20:30, Virgil <virg...@nowhere.com> wrote: > > >> And there are in any maximal infinite binary tree paths that are not > >> members of any countable set of paths, as Cantor proved. > > > Then let me know one of those paths, please. I will tell you, whether > > it belongs to a counatble set. > > > Regards, WM > > Your quantifier confusion is showing again.
Your belief in matheological nonsense is showing again. > > For any path in the complete maximal binary tree, there is at least one > countable set of paths that contains it. (Trivially, the set {p} > contains the path p for every path p. The union of {p} and the set of > terminating paths is a countably infinite set which contains p.) > > For any countable set of paths, there is at least one path in the tree > that is not in that set.
Your belief in matheological nonsense is showing again. You claimn also: "For any list of binary sequences, there is at least one binary sequence that is not in that list"?
The tree is constructed from the list of terminating sequences in the form of terminating paths. This list does not contain the path 0.111... Hence the union of terminating paths, namely the tree, does not contain that path 0.111...
You cannot distinguish it from all paths of the tree because 0.111... does not contain any digit that is not in a "path" of the list, together with all its preceding digits. > > Consider the set of terminating rooted paths: it is a countable > infinite set (its elements can be put in 1-to-1 correspondence with the > natural numbers), and missing every non-terminating rooted path, as > well as every (terminating or non-terminating) non-rooted path. > > Describe a countable set of paths that you believe contains every path > in the complete maximal binary tree.
The set of all terminating paths extended by tails 000... contains all nodes and all combinations of nodes that can act as paths in the tree.
