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. > > 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.
> 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).
The explanation is as follows: In order to define p_0 as a binary sequence, you say that for every terminating path p_n there is an m > n such that the node m is covered by p_0 but not by p_n. In the complete binary tree however, we have all nodes already covered by terminating paths. Therefore this bad trick of logic (using potential infinity for a set of nodes that should have actual existence) fails.
