Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 12/16/24 6:28 AM, WM wrote:

On 16.12.2024 11:23, Mikko wrote:

On 2024-12-15 11:33:15 +0000, WM said:

 

>
We cannot name dark numbers as individuals.

>
We needn't. The axioms of natural numbers ensure that every natural number
has a successor,

 The set, i.e. all numbers together, has no successor. That is a necessary condition for using all with no exception. That must happen according to
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}.
 

If that is not possible then there are no
natural numbers.

 That is not possible for an actually infinite set. It is only possible for numbers coming into being.
 Regards, WM
 

No, if you actually have that actually infinite set, they are all there to begin with, but of course, you can't make that infinite set with your finite logic, so you just can't handle such a set.