Date: Dec 13, 2012 5:49 AM
Author: Zaljohar@gmail.com
Subject: Re: On the infinite binary Tree
On Dec 13, 9:56 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> It is nonsensical because the same could be assumed for Cantor's

> diagonal. It would be undefinable and it would be impossible to prove

> that it differs from all lines of the list - in particular if

> undefinable reals exist and are members of the list.

>

Of course the diagonal in some cases can be non-definable, that is

well known. For example take the set of all definable reals (which is

countable), take any bijective function F between the set of all

definable reals and the set N of all naturals, then F must be non-

definable, since if F was definable then the antidiagonal on it would

a definable real that is not in the list of all definable reals which

cannot be. And so the anti-diagonal includes F in the formula defining

it, but F is a non definable parameter so the Anti-diagonal is not a

parameter free definable and thus as we say non definable.

That doesn't mean that we cannot prove it is different from all reals

in the list, on the contrary we don't need parameter free definability

in order to determine that the diagonal is different from the reals in

the original list, we can do that without it, as Cantor did.

Your error is that you think too much of non definability. It is not

so destructive as you think.

Zuhair