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.
