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 <vir...@ligriv.com> wrote:
>> In article
>> <0190d864-1253-4b32-9620-d92a5d0cb...@u5g2000pbs.googlegroups.com>,
>> "Ross A. Finlayson" <ross.finlay...@gmail.com> 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
humor.

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
infinity.

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.