```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-definablereal 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 haveseen 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 definablereals is 0. If most reals are non-definable, why must all reals ofevery Cantor list always be definable? If all reals of the list aredefinable, then they belong to a countable set. Then we cannot proveuncounatbility. Or can we prove that the set of definable reals isuncountable - because it is countable but there are, somewhere else,undefinable "reals"?Regards, WM
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