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Topic: Matheology § 190
Replies: 15   Last Post: Jan 14, 2013 3:35 PM

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mueckenh@rz.fh-augsburg.de

Posts: 14,740
Registered: 1/29/05
Re: Matheology § 190
Posted: Jan 14, 2013 4:28 AM
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On 14 Jan., 00:12, Virgil <vir...@ligriv.com> wrote:

> > Every distance is finite. There is no distance that is
> > larger than every finite distance. All finite distances are countable.

>
> Irrelevant!


In matheology solid arguments are of little value.

> Any (complete) path in a Complete Infinite Binary Tree
> contains infinitely many nodes and infinitely many branchings, and
> cannot be distinguished from all other (complete) paths without
> specifying at least infinitely many of its nodes or its entire sequence
> of branchings.


But that is impossible unless one of countably many finite
specifications is used.
>
> In reality it is relevant, since any (complete) path in a Complete
> Infinite Binary Tree contains infinitely many nodes and infinitely many
> branchings, and cannot be distinguished from all other (complete) paths
> without specifying at least infinitely many of its nodes or its entire
> sequence of branchings


which is impossible unless the God of matheology will help or a finite
definition of countably many is applied.
>
> Note that while a finite number of nodes can separate one path from any
> finite set of other paths and from some infinite sets of other paths, it
> takes infinitely many nodes to separate it from EVERY other path,


alas that number is not available, unless ...

Regards, WM



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