In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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.
WM conflates the set of all FISONs with the union of that set, |N, so, as he does far too often, fails to distinguish between the subsets of a set and the members of a set.
Until he has learned ro distinguish between the members of a set and the subset of a set reliably, he should avoid anything to do with sets.
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.
I never said that they were impossible to distinguish by node, because they are.
In a Complete Infinite Binary Tree, every binary rational path has only finitely many left-child nodes or only finitely many right-child nodes, whereas every other path has infinitely many of each.
Something that everyone who understands anything about Complete Infinite Binary Trees should know but WM apparently does not. --