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 ofhumor.If you get a book on automata, where distinguishability is givenformal definition, you will find that it is hierarchicallydefined as k-distinguishability for each k.  To be indistinguishable,that is to be identified as an individual, requires a completedinfinity.That two given *infinite* sequences of symbols can be distinguishedat some finite step does not mean that a finite initial segmentis an individual.  It is a reference to the class of individualshaving the same initial segment.