Date: Mar 30, 2013 6:45 PM
Subject: Re: Matheology § 224
On 30 Mrz., 19:15, Virgil <vir...@ligriv.com> wrote:
> In article
> 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.