On 14 Jan., 00:12, Virgil <vir...@ligriv.com> wrote:
> > Every distance is finite. There is no distance that is > > larger than every finite distance. All finite distances are countable. > > Irrelevant!
In matheology solid arguments are of little value.
> Any (complete) path in a Complete Infinite Binary Tree > contains infinitely many nodes and infinitely many branchings, and > cannot be distinguished from all other (complete) paths without > specifying at least infinitely many of its nodes or its entire sequence > of branchings.
But that is impossible unless one of countably many finite specifications is used. > > In reality it is relevant, since any (complete) path in a Complete > Infinite Binary Tree contains infinitely many nodes and infinitely many > branchings, and cannot be distinguished from all other (complete) paths > without specifying at least infinitely many of its nodes or its entire > sequence of branchings
which is impossible unless the God of matheology will help or a finite definition of countably many is applied. > > Note that while a finite number of nodes can separate one path from any > finite set of other paths and from some infinite sets of other paths, it > takes infinitely many nodes to separate it from EVERY other path,