On 14 Apr., 02:24, Virgil <vir...@ligriv.com> wrote:
> > All your examples are finite definitions. > > Nothing in either mathematics nor logic prohibits finite definition of > infinite processes or procedures.
No, finite definition isn't prohibited. But it does not prove the existence of actual infinity. > > > Neither these nor the paths > > of the Binary Tree can be used to distinguish more than countably many > > numbers. > > Distinguishability is not a requirement or prerequisit for existence, at > last not outside Wolkenmuekenheim.
How can you apply the axiom of extensionality forall A forall B (forall X (X e A <==> X e B) ==> A = B) if you cannot distinguish an element X from the other elements of A or B? > > > But undistinguishable numbers are not numbers that can be > > used to distinguish things (Dedekind). > > It is only their existence, not their distinguishability, that is at > issue.
That is a theorem of religion with respect to Gods and Goddesses: They exists, independent of our knowledge.