Date: Mar 31, 2013 12:00 PM
Author: fom
Subject: Re: Matheology § 224

On 3/31/2013 10:44 AM, Ross A. Finlayson wrote:
> On Mar 30, 10:35 pm, Virgil <> wrote:
>> In article
>> <>,
>> "Ross A. Finlayson" <> wrote:

>>>> Something that everyone who understands anything about Complete Infinite
>>>> Binary Trees should know but WM apparently does not.
>>>> --

>>> Those aren't all the rational sequences, only integral products of
>>> negative powers of two.

>> Any product, integral or otherwise, of negative powers of two is a
>> negative power of two.
>> --

> Those aren't all the rational sequences: only the products of
> integers and negative powers of two. (Here they're well enough
> integral products.)
> Any path with sub-path ((0|1)+)\infty is also a rational sequence.
> Paths are distinguishable by their nodes, and distinguished by their
> nodes: there are countably many.
> Regards,
> Ross Finlayson

Funny. Glad to see you still have a sense of

If you get a book on automata, where distinguishability is given
formal definition, you will find that it is hierarchically
defined as k-distinguishability for each k. To be indistinguishable,
that is to be identified as an individual, requires a completed

That two given *infinite* sequences of symbols can be distinguished
at some finite step does not mean that a finite initial segment
is an individual. It is a reference to the class of individuals
having the same initial segment.