On 11 Jun., 15:36, William Hughes <wpihug...@hotmail.com> wrote: > On Jun 11, 9:19 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 11 Jun., 13:00, William Hughes <wpihug...@hotmail.com> wrote: > > > > > Because paths cannot be distinguished without nodes. > > > > Proves nothing. We know that a countable > > > number of elements can distinguish an uncountable > > > number of subsets. A countable number of nodes can > > > distinguish an uncountable number of paths. > > > No that is provably wrong. All nodes are used up by a countable number > > of paths, e.g., all paths ending in a tail of zeros. Therefore no > > possibility exists to construct or to distinguish by one or many or > > infinitely many nodes of the tree another path. > > Your claim is that "no possibility exists" > > Nope. In any tree, any node that is not a leaf node > can contribute to more than one path. The possibility > exists to construct another path using nodes > which are not leaf nodes.
If you have a tree that is (the nodes of which are) completely covered by a set of paths then you cannot show any node that will distinguish a further path from that given set of paths. But if you cannot distinguish a path from a given set of paths, then it belongs to that set.