On 21 Dez., 17:36, Zuhair <zaljo...@gmail.com> wrote: > On Dec 21, 2:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > And they are not definable with parameters either. > > Do you mean that the bijection between the set of all naturals and the > set of all finite words is NOT definable at all, whether with or > without parameters?
No, this bijection has obviously been defined. What is no definable is a set with uncountably many elements, or, better: What is not definable are uncountably many elements. (The set is definable, yet not exististing free of contradictions.)
Note finally: Every Cantor diagonal r differs from any other real number by a finite initial segment n(r) of its string of digits. That is not possible with the Binary Tree. A diagonal does not differ from all finite paths, i.e., for every initial segment n(r) of every real number r there exists a finite path of the Binary Tree that is n(r). You may consider actual infinity as well as uncountable languages, but that does not change the fact that Cantor's argument does not apply.