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.