Date: Dec 28, 2012 12:14 PM
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.