On 12 Jun., 22:23, Virgil <virg...@nowhere.com> wrote:
> > > Sorry, that is impossible. Every node of path p and every set of nodes > > of path p is covered by one or more paths of P. > > Is P a set of paths or merely a set of nodes?
It is a set of paths. > > If it is a set of paths, then it must contain all uncountably many paths > or there will be a path which is not member of it.
Wrong. All countably many terminating paths are sufficient to cover all nodes of the tree. > > > > > > So it is possible to contruct another path, p, which can be > > > distinguished from every element of P. > > > That is impossible. The path p_0 = 0.111... for instance is completely > > covered by terminating paths, whether or not it had been inserted > > originally. > > If P is only a set of terminating paths then no non-terminating path > will be a member of it.
All non-terminating paths are in the tree constructed by P.