Date: Mar 25, 2013 5:33 PM
Subject: Re: Matheology § 224

On 25 Mrz., 21:35, Virgil <> 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