In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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!
And false. The set of all finite distances is the set of non-negative reals which is uncountable. > > In matheology solid arguments are of little value.
In WMytheology you mean! > > > 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.
That would only mean that some of them cannot be distinguished from all others, at least in WMytheology . > > > > 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.
True mathematics, unlike WMytheology, has no gods, and needs none. > > > > 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, > > alas that number is not available, unless ...
In standard mathematics inaccessible things may have to exist because things like Complete Infinite Binary Trees can exist.
In WMytheology no such thing as a Complete Infinite Binary Tree can exist at all, so that all WM's claims about them are lies.