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Topic: Distinguishability of paths of the Infinite Binary tree???
Replies: 69   Last Post: Jan 4, 2013 11:11 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Distinguishability of paths of the Infinite Binary tree???
Posted: Dec 26, 2012 6:03 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 26 Dez., 13:24, gus gassmann <g...@nospam.com> wrote:
> > On 26/12/2012 7:29 AM, Zuhair wrote:
> >
> >
> >

> > >> Depends on the level of distinguishability at issue.
> >
> > >> For any finite set of such strings, finite initial segments suffice to
> > >> distinguish all of them from each oterhbut for at least some infinite
> > >> set, no finite set of finite initial segments suffices.

> >
> > > Yes but a countable set of them suffices! no?
> >
> > Of course. And how many such countable sets are there? Cantor showed
> > that there are uncountably many.

>
> Cantor showed that by digits or nodes.

Since while sets may have members they need not ever contain either
digits or nodes, Cantor did no such thing.

> And I showed

The only thing you evern sow is your own ignorance.
> >
> > There are at least two counter-intuitive notions when dealing with
> > infinities: There is an infinite set, each of whose elements are finite
> > (viz. the sequence of initial segments {{1}, {1,2}, {1,2,3}, ...}; and
> > the set of all countable subsets of a countable set is uncountable. The
> > only thing this shows is that intuition is sometimes insufficient to
> > grasp complex things.

>
> No, it shows that there is no nonsense great enough for matheologians

Like WM

> not to believe in

> No set of finite subsets of |N exists, that was uncountable.

Do you mean that now there are some which have now become uncountable?

> Only a subset containing uncountably
> many infinite subsets is uncountable.

Right! And in ZFC, for example, such sets must exist.
>
> Cantor's and Hessenberg's "proofs" simply show that infinity is never
> finished and a complete infinite set is not part of sober thinking.

Thinking about infiniteness certainly makes WM extremely unsober.
--

Date Subject Author
12/23/12 Zaljohar@gmail.com
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/24/12 mueckenh@rz.fh-augsburg.de
12/24/12 Virgil
12/25/12 mueckenh@rz.fh-augsburg.de
12/25/12 Virgil
12/26/12 mueckenh@rz.fh-augsburg.de
12/26/12 Virgil
12/26/12 mueckenh@rz.fh-augsburg.de
12/26/12 Virgil
12/27/12 mueckenh@rz.fh-augsburg.de
12/27/12 Virgil
12/28/12 mueckenh@rz.fh-augsburg.de
12/28/12 Virgil
12/29/12 mueckenh@rz.fh-augsburg.de
12/29/12 Virgil
12/30/12 fom
12/30/12 mueckenh@rz.fh-augsburg.de
12/30/12 fom
12/30/12 Virgil
12/30/12 ross.finlayson@gmail.com
12/30/12 Virgil
12/30/12 ross.finlayson@gmail.com
12/30/12 Virgil
12/30/12 ross.finlayson@gmail.com
12/30/12 Virgil
1/4/13 ross.finlayson@gmail.com
12/30/12 forbisgaryg@gmail.com
12/30/12 ross.finlayson@gmail.com
12/30/12 Virgil
12/26/12 Zaljohar@gmail.com
12/26/12 Virgil
12/26/12 Zaljohar@gmail.com
12/26/12 gus gassmann
12/26/12 mueckenh@rz.fh-augsburg.de
12/26/12 Zaljohar@gmail.com
12/27/12 mueckenh@rz.fh-augsburg.de
12/27/12 Zaljohar@gmail.com
12/28/12 mueckenh@rz.fh-augsburg.de
12/28/12 Zaljohar@gmail.com
12/28/12 Virgil
12/29/12 Zaljohar@gmail.com
12/29/12 Virgil
12/29/12 mueckenh@rz.fh-augsburg.de
12/29/12 Virgil
12/28/12 Zaljohar@gmail.com
12/29/12 mueckenh@rz.fh-augsburg.de
12/29/12 Virgil
12/27/12 Virgil
12/26/12 fom
12/26/12 Virgil
12/26/12 fom
12/26/12 Virgil
12/26/12 mueckenh@rz.fh-augsburg.de
12/26/12 Virgil
12/26/12 mueckenh@rz.fh-augsburg.de
12/26/12 forbisgaryg@gmail.com
12/26/12 Virgil
12/26/12 fom
12/27/12 gus gassmann
12/27/12 Tanu R.
12/27/12 mueckenh@rz.fh-augsburg.de
12/27/12 Tanu R.
12/27/12 Virgil
12/28/12 Zaljohar@gmail.com
12/28/12 Virgil
12/27/12 fom
12/27/12 Virgil
12/24/12 Ki Song