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.