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.