In article <1f069edc-4bee-4740-a0d5-4756d70b2738@j32g2000yqh.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 17 Jun., 18:09, William Hughes <wpihug...@hotmail.com> wrote: > > Your claim is that "no possibility exists to construct or to > > distinguish by one or many or infinitely many nodes > > of the tree another path." > > > > A: actually infinite paths exist, > > B: the infinite tree contains a path p that can be > > distinguished from every path of P. > > > > You agree > > > > A ==> B > > > > So if A is true your claim is false. > > The claim is false if and only if you can distingusih a path p from > all pats from the set P when written in form of the tree.
Since P is NOT a set of nodes, it cannot be "written in the form of a tree". Its union can be so written, provided that that union contains all nodes of the tree, but then one has lost the original path structure.
> > > > The subset of nodes that is now in the tree is > > > > > > t={1,11,111, ...} > > There is no sequence of 1's added that is longer than every such > sequence of paths in P.
Sequences of paths are irrelevant. No such "sequence" of paths can contain its "limit" unless the sequence is eventually constant. In which case it essentially contains only one path. > > > > > > Note that t is not an element of P, so the subset > > > > t is never added to the tree. > > > > Which is the first statement you disagree with > > > > all nodes of t are in the tree > > t is in the tree > > all nodes of t are in P > > t is not an element of P > > I disagree with the statement: More nodes of t are in tree than are in > any single path of P.
Since no one has said it, except you, why are you bothering disagree?
> > > > Note: if all the nodes of a path h are in the > > tree then h is in the tree, however, if all the > > nodes of h are in P, h may or may not be an element > > of P. > > Wrong. The list of paths of P is the tree in slightly different > notation.
Notation does not affect membership.
If there are paths not in P according to one notation, which there are, then no change of notation can change that.
> When changing from list to tree, then several bits are > mapped on one node, not the other way round. That number does > decrease, not increase. Again you are trying to rape logic.
On the contrary. WE are not the ones who claim that change of notation induces a change in membership.
If anyone is trying to rape logic, it is WM, with us defending her honor.
