In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 17 Jun., 21:20, William Hughes <wpihug...@hotmail.com> wrote: > > > > Why should the subset belong to one element of the list of > > > paths > > > > It doesn't. > > "the tree contains a subset of nodes that is > > *not* contained in one element of the list of paths" > > As it is neither contained in a path of the tree, this observation is > completely irrelevant.
If the original list of paths is no more than countable and the tree is a maxima; infinite binary tree, then there are necessarily paths in that tree not in the list. This is so because countably many paths can cover all nodes but cannot cover all paths, as Cantor proved.