Date: Dec 28, 2012 12:14 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Distinguishability of paths of the Infinite Binary tree???

On 27 Dez., 19:04, Zuhair <zaljo...@gmail.com> wrote:
> On Dec 27, 3:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>

> > Here is a parameter free enumeration of all finite initial segments of
> > the paths of the Binary Tree:

>
> > 0
> > 1, 2
> > 3, 4, 5, 6
> > 7, ...

>
> > Regards, WM
>
> Show me a parameter free formula "phi(y)" where the alleged
> enumeration you've just depicted above is defined after i.e. suppose
> your enumeration is denoted as "En" then show me that: For all y. y in
> En iff phi(y).
> Remember parameter free formula phi(y) means a formula in which ONLY y
> occurs free. If you show that then I'd agree with you. If you don't
> show that, then you didn't prove that your alleged enumeration is
> parameter free. AND please spare me any responses that gives a
> different definition for the term "parameter free definable" that you
> have in your mind since simply it is not relevant to the "parameter
> free definable" concept that I'm speaking about.


It not obvious to me, what you call parameter-free. (And you need not
explain it, because I am not interested in your interpretation.) But
it is obvious to me that Cantor enumerated the rational numbers just
like I enumerate the finite paths of the Binary Tree. And he
enumerated the digits of the diagonal in just the same way, namely
assuming the complete existence of all natural numbers.

Regards, WM