In article <63e6a071-5071-41b2-a0dd-2df7e53372cb@g1g2000yqh.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 12 Jun., 17:42, William Hughes <wpihug...@hotmail.com> wrote: > > On Jun 12, 10:36 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 12 Jun., 12:23, William Hughes <wpihug...@hotmail.com> wrote: > > > > > > On Jun 12, 3:14 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 11 Jun., 23:06, William Hughes <wpihug...@hotmail.com> wrote: > > > > > > > > On Jun 11, 4:38 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > On 11 Jun., 21:33, 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." > > > > > > > > Before P is used to construct the binary tree, > > > > > > the binary tree contains a path > > > > > > p that can be distinguished from > > > > > > every element of P. > > > > > > > Yes > > > > > > Using P to construct the binary tree does > > > > not change any of the elements of P > > > > or the path p. > > > > > > Please acknowledge > > > > > > After P is used to construct the binary tree, > > > > the binary tree contains a path > > > > p that can be distinguished from > > > > every element of P. > > > > > After construction, the tree contains P (and every other path of the > > > unit interval you wish) in same same form > > > > So after construction the tree contains every element of > > P and the path p. Since they have not changed form it > > is still possible to distinguish p from every element of P. > > Sorry, that is impossible. Every node of path p and every set of nodes > of path p is covered by one or more paths of P.
Is P a set of paths or merely a set of nodes?
If it is a set of nodes, it must be the set of all nodes or there will be paths wish are to subset of it. and the it will contain as subsets uncountably many paths
If it is a set of paths, then it must contain all uncountably many paths or there will be a path which is not member of it.
> > > > So it is possible to contruct another path, p, which can be > > distinguished from every element of P. > > That is impossible. The path p_0 = 0.111... for instance is completely > covered by terminating paths, whether or not it had been inserted > originally.
If P is only a set of terminating paths then no non-terminating path will be a member of it.
If P is a set of nodes, then it must contain every node of every finite subtree, and thus have every one of those uncountably many paths as a subset. Otherwise there will be paths that it does not contain as subsets. > > > This directly contradicts your claim > > > > "no possibility exists to construct or to > > distinguish by one or many or infinitely many nodes > > of the tree another path." > > Sorry, this claim still stands. The reason is, that the path 0.111... > does not exist. It is nothing but a union of terminating paths > (potential infinity).
Except that if the infinite tree exists at all, which has been conceded or we would not even be talking about it, then it is actually infinite and WM's finiteness restrictions no longer apply.
Wm cannot concede the existence of an actually infinite tree, which he has been doing, and then insist that it does not have the properties of an actually infinite tree.
