Date: Mar 30, 2013 9:09 PM
Subject: Re: Matheology � 224
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
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.