In article <email@example.com>, firstname.lastname@example.org wrote:
> On Saturday, 20 July 2013 00:30:19 UTC+2, Virgil wrote: > > >> If you define the Binary Tree that contains only all finite initial > >> segments of its infinite paths > > > Unless those infinite paths all actually existed, it would be nonsense to > > speak of finite initial segments of them. > > Even if they don't exist, matheologians know what I mean with their FIS. > Since I speak to matheologians, this is fine.
If WM is speaking only to matheologians, i.e., occupants of WM's wild weird world of WMytheology, It is no wonder that he does not make any sense to those of us not so incarcerated. > > So answer: How can we distinguish this Binary Tree that contains only all FIS > of the paths of his big brother from his big brother?
Outside of WM's wild weird world of WMytheology, no such incomplete tree can exist. Any tree containing all FIS of the paths of a proper COMPLETE INFINITE BINARY TREE, will contains infinite paths as well as all those FISs of infinite paths.
Just as for sets of naturals, any set of naturals containing all FISONs must be |N, the set of all naturals. --