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Topic: On the infinite binary Tree
Replies: 64   Last Post: Dec 17, 2012 11:06 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: On the infinite binary Tree
Posted: Dec 13, 2012 6:49 PM

In article
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

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.
--

Date Subject Author
12/12/12 Zaljohar@gmail.com
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 trj
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Virgil
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/14/12 Zaljohar@gmail.com
12/14/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Tanu R.
12/14/12 Virgil
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/12/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/12/12 george
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 george
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Tanu R.
12/14/12 Virgil
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/15/12 Tanu R.
12/14/12 Charlie-Boo
12/14/12 forbisgaryg@gmail.com
12/15/12 ross.finlayson@gmail.com
12/15/12 forbisgaryg@gmail.com
12/15/12 ross.finlayson@gmail.com
12/16/12 forbisgaryg@gmail.com
12/17/12 ross.finlayson@gmail.com
12/16/12 Ciekaw
12/16/12 Virgil