On 30 Mrz., 19:15, Virgil <vir...@ligriv.com> wrote: > In article > <ab85409a-eabf-4b68-b505-d194ed33a...@c15g2000vbl.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 30 Mrz., 10:17, William Hughes <wpihug...@gmail.com> wrote: > > > On 24 Mrz., 18:09, WM <mueck...@rz.fh-augsburg.de> wrote: > > > <snip> > > > > > > The only difference is that in the second case you consider > > > > > some subsets of the nodes to be paths, that are not considered > > > > > to be paths in the first case. > > > > > Well, that is a correct description. It implies that these additional > > > > subsets cannot be distinguished by nodes from the finite subsets > > > > Piffle. It is trivial to distinguish a subset that has a node > > > at a last level from a subset that does not have a node > > > at a last level. > > > No, that is impossible if an infinite path consists of infinitely many > > finite subsets. > > All infinities consist of infinitely many finite parts. > But the infinite set of all naturals is distinguishable be from the > infinite set of all FISONs,
And so is the path of 1/pi distinguishable from all its finite initial segments which are in the tree. But as you said, 1/pi is not distinct from them. It comes into tze construction automatically. The limit is in any case a member of the sequence. That is unmathematical. > > > It is impossible to distinguish the actually infinite path of 1/pi > > from a path that only is built of all finite initial segments of the > > path of 1/pi. > > It may be so in Wolkenmuekenheim, but a set of only finite > approximations to an irrational number can elsewhere be distinguished > from the number itself.
Then explain why this is not possible in the Binary Tree. You said that the irrationals come into the tree automatically, impossible to distinguish by nodes.