Date: Mar 25, 2013 5:33 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 25 Mrz., 21:35, Virgil <vir...@ligriv.com> wrote:

> > 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?

>

> That depends on what WM means by a "rational path".

That is a path that represents a rational number in binary.

>

> If what WM means is a path in an infinite binary tree which has only

> finitely many branchings in one of the two directions, any tree with all

> possible such paths will also have "irrational" paths as a sort of

> "limit path"

So the set of all rational numbers always contains all irrational

numbers? Or only some? Or is that a speciality of the Binary Tree?

Regards, WM