On 17 Mrz., 00:25, Virgil <vir...@ligriv.com> wrote:
> > > Can WM provide an definition for natural numberss which doe not state, > > > or at least imply, that every natural must have a successor natural? > > > Numbers are creations of the mind. Without minds there are no numbers. > > Which is not a relevant answer.
By definition of a matheologian. > > Can WM provide an definition for natural numbers which doe not state, > or at least imply, that every natural must have a successor natural?
It is always stated or at least implicitly assumed in classical mathematics that we are able to add 1. In reality this is an erroneous assumption as has been shown in MatheRealism. > > > you are not able to write aleph_0 digits of a real numbers like 1/9. > > So what? There are lot of things in mathematics one cannot do, but that > should not keep us from doing what we can do, the way you would limit us.
But the claim of matheology is that all digits exist and can be determined - for instance all digits of pi. And that is simply wrong, because you never get more than finitely many, such that always infinitely many must remain unknown.
Of course distinguishing the elements of uncountable sets requires that possibility. And if it turns out impossible, then prayers are issued - like the axiom of choice. Such praying and believing is part of theology and matheology.