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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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 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Distinguishability of paths of the Infinite Binary tree???
Posted: Jan 4, 2013 11:11 PM

On Dec 30 2012, 1:44 pm, "Ross A. Finlayson"
<ross.finlay...@gmail.com> wrote:
> On Dec 30, 1:15 pm, Virgil <vir...@ligriv.com> wrote:
>

> > In article
> >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>
> > > > requires that they be listable, but one can prove that they are not
> > > > listable by showing that no list of them can be complete.
> > > > And no mater how vociferously WM tries to argue otherwise, in standard
> > > > mathematics that can all be done.
> > > > --

>
> > > Well, not when "standard" was "pre-Cantorian"
>
> > I used only the present tense which eliminates pre-Cantorianism.
> > --

>
> Then you shouldn't discount the future where, as we know modern
> mathematics is incomplete, there are to be discovered true things
> about its domain, not its theorems.
>
> And no, there's no proof that ZF (as a general foundation for modern
> mathematics) is consistent and complete, and there aren't that it's
> consistent, either, and Goedel shows, in modern mathematics, it's not
> both.  And, measure theory uses countable additivity (of the non-
> finite non-zero infinitesimal differential patches) for real analysis,
> and concrete mathematics uses asymptotics and sometimes, regular
> infinite ordinals:  with no applied results solely due transfinite
> cardinals, and indeed transfinite set theory is somewhat a raw,
> disposed shoehorn of real analysis.  And half of the integers are
> even.
>
> Let's work more on posts, and progress, than replies.  Quit worrying
>
> And as described above, a breadth-first traversal, sees different
> results for the tree's "anti-diagonal", as that it's simply at the end
> of the traversal, end-to-end, point-to-point.
>
> Then the question arises, diagonal of what?  Where's the middle?
> Where's the square.
>
> Draw a line:  without putting pencil to paper.  That's mathematics.
>

Rather casually: rays through ordinal points.

Draw the binary tree with the endpoints of the paths of the finite
tree to points 0, ..., 2^n-1.

Consider rays from the origin, to the ordinal points 0, ..., 2^n-1.
They are countable.

Then with rays from the origin through 0, ..., 2^w-1, they are
countable.

Are not the rays dense in the paths?

Regards,

Ross Finlayson

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