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

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Virgil

Posts: 7,021
Registered: 1/6/11
Re: On the infinite binary Tree
Posted: Dec 13, 2012 5:50 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
<a618812f-4c3c-4703-838c-7cafe1060c59@fn10g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 13 Dez., 21:02, Zuhair <zaljo...@gmail.com> wrote:
> > On Dec 13, 3:56 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >

> > > 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
> >
> > Cantor's list do contain non definable reals.


The more formal , and instructive, name for them is "inaccessible
numbers". They are the numbers that, to make the reals uncountable must
exist, but are beyond the power of mathematics to be individually
accessed. We cannot access more than countably many reals.

And since they cannot be accessed, they cannot appear in any lists.
>
> Which one in what line? What is the corresponding digit of the
> diagonal?
>

> > Actually some diagonals
> > of Cantor's are non definable.

>
> Lists containing undefinable entries do not supply diagonals at all.


But such a list would have to contain inaccessible numbers which means
they would have to be accessible after all. Contradiction.
>
> > The bijective function between all
> > definable reals and the set N of all naturals is NON definable set!


The problem is that every such list will define numbers not listed in it.
>
> That is completely without interest.


What is of no interset t WM is usually the very thing proving him wrong
again.
> >
> > Note: definable is short for "definable by parameter free finite
> > formula"

>
> No. Definable means "definable by a finite word". Everything else is
> "undefinable".


Accessible and inaccessible are related, but better, representations of
the relevant ideas.
>
> Regards, WM

--




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

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