On 24 Mrz., 23:13, "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > 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?