Date: Mar 25, 2013 7:45 AM
Subject: Re: Matheology § 224
On 24 Mrz., 23:13, "Ross A. Finlayson" <ross.finlay...@gmail.com>
> On Mar 24, 2:51 pm, fom <fomJ...@nyms.net> wrote:
> > On 3/24/2013 4:34 PM, WM wrote:
> > > On 24 Mrz., 21:29, Virgil <vir...@ligriv.com> wrote:
> > >> In article
> > >> <729f073f-8948-4eb9-991a-2bd249ac5...@c6g2000yqh.googlegroups.com>,
> > >> A binary tree that contains one path of each positive natural number
> > >> length will necessarily also contain exactly one path of infinite length.
> > > Like the sequence
> > > 0.1
> > > 0.11
> > > 0.111
> > > ...
> > > that necessarily also contains its limit?
> A binary tree that contains one path, of all zero-branches, of each
> finite length, will necessarily contain a path of 0-branches of
> infinite length.
If actual infinity exists. Otherwise it contains nothing more than all
finite paths. But here is a question that is easier to answer and to
decide: Does the Binary Tree that contains all rational paths also
contain all irrational paths?