Date: Dec 13, 2012 7:56 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: On the infinite binary Tree
On 13 Dez., 11:49, Zuhair <zaljo...@gmail.com> wrote:

> 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.

Also the elements of the list could be non-definable, if non-definable

real numbers existed.

> 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.

Cantor did not accept non-definable reals. If he had, he would have

seen that his proof fails.

>

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

> so destructive as you think.

No? Nearly every real number is undefinable. The measure of definable

reals is 0. If most reals are non-definable, why must all reals of

every Cantor list always be definable? If all reals of the list are

definable, then they belong to a countable set. Then we cannot prove

uncounatbility. Or can we prove that the set of definable reals is

uncountable - because it is countable but there are, somewhere else,

undefinable "reals"?

Regards, WM