```Date: Dec 13, 2012 6:49 PM
Author: Virgil
Subject: Re: On the infinite binary Tree

In article <d9d2da33-b039-4af6-bfff-6dfc8efe8857@r3g2000vbn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 13 Dez., 20:47, Zuhair <zaljo...@gmail.com> wrote:> > > > Cantor did not accept non-definable reals. If he had, he would have> > > seen that his proof fails.> >> > No Cantor's proof survives non parameter free definability. We don't> > need every real to be definable by a parameter free formula in order> > for Cantor's proof to go through.> > Wrong. Undefinable reals are undefinable. Completely undefined. But> that is of little interest. Our concern is that the Binary Tree> contradicts Cantor's proof.WM's allegedly complete  infinite binary trees are never incomplete.Every subset of N should correspond to a different path, the one branching left at just those levels whose numbers are in the set, and right at all other levels. and N has more subsets than WM's tree has paths.> > > > That's your simple mistake, you> > think Cantor's proof requires that all reals must be parameter free> > definable, but this is not the case. Cantor's proof works in a> > flawless manner even if MOST of the reals are non parameter free> > definable.> > At least if we want to know the diagonal, we need every line to be> excplicitly defined. Not true. The argument is perfectly valid so long as all its entries are defineable, but does not need any of them explicitely defined. > And in fact most of the reals are undefinable.Enough are defineable!> > > Actually Cantor's proof mounts to the conclusion that MOST> > reals are non parameter free definable reals, of course he saw that,> > this is obvious really.> > Obvious is only that you have no idea of that matter. While that is true enough foe WM, it is not so in general.--
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