In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 19 Jun., 13:47, William Hughes <wpihug...@hotmail.com> wrote: > > > A subset of nodes is distinguished from every > > element of P that you can specifically address > > if and only if it is not contained in > > a single element of P that you can specifically > > address. > > > > and you have agreed that t can be distinguished from > > every element of P. > > It does not matter whether I have agreed, it matters whether it is > true.
And as WM has no access to truth, except by accident, and even then he may well reject it, one is better advised to go elsewhere to find it.
> As you see from the tree, it is not true, unless the transformation > from the list to the tree would introduce new paths.
Which it does. To get from a set of paths to a tree, one bmust take the union of the set of paths as the set of nodes of that tree, and that set of nodes contains subsets, including paths, that were not members of the original set of paths.
WM has demonstrated this himself, though without realizing what he has shown:
Wm starts with the set of all infinite binary sequences of 0 and 1 nodes which contain only finitely many one nodes. The the union of this set of sets is the set of all nodes of a maximal infinite binary tree, so is such a tree. But in that tree there are maximal totally ordered by "ancestor of" sets of nodes, i.e., paths, which contain infinitely many 1 nodes, so are NOT members of WM's original set of paths.
That, however, > would be something between mathemagic and matheology. Under any > circumstances that is rubbish.
It is WM's own personal rubbish then, since WM is the one who presented us with that set of paths and that tree.