In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
Nor prove the nonexistence of actual infinitenes > > > > > 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?
That there may be two representations of sets which are somehow equal as sets but not provably equal does not create an innsurmountable problem, at least not outside of Wolkenmuekenheim.
It is well known that not everything true need be provably true. > > > > > 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. > > Mathematics runs in a different manner.
A far different manner from any manner WM presents in sci.math. --