In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> > > Irrelevant. You do not distinguish p from the tree. > > You distinguish p from every element of P. > > You cannot distinguish p from every path of the tree. > Every path of the tree is is from P.
Not if one can count the paths of P, since on cannot count the path of a maximal infinite binary tree. > > > > > P contains every subset of nodes of the binary tree.
P, being a set of sets of nodes, would have to be the powerset of the set of all nodes to have as a member EVERY set of nodes, but since the set of nodes is countably infinite, that makes P, the set of all its subsets, uncountably infinite.