Re: The non-existence of "dark numbers"

On 14.03.2025 16:21, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

Perhaps everybody is unable to see that
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo?

 Everybody can see that, and everybody but you can see it has nothing to
do with the point it purportedly answers.

ℕ_def contains all numbers the subtraction of which from ℕ does not result in the empty set. Obviously the subtraction of all numbers which cannot empty ℕ cannot empty ℕ. Therefore |ℕ \ ℕ_def| = ℵo. Do you agree? If not, it is useless to discuss with you.

Wrong.  It is an "instantaneous" definition which completes N.

Yes, of course. But ℕ_def is not completed by its definition.

 There are
not various stages of "N" which are in varying stages of completion.

ℕ_def is never complete.

There is place to strive or tend.

 The tending takes place, but not in a "place".

No? Tending means that hitherto undefined natural numbers become defined. That takes place on the ordinal line.

That I have to write such
nonsense to answer your point shows the great deterioration which has
taken place in a once vital newsgroup.

Hardly to believe that matheology like tending of ordinals outside of the ordinal line has ever been useful.

 

Yes, they cannot be determined as individuals.

 They don't exist, as I have proven.

You have proven that you are a matheologian with little ability to understand arguments contradicting your matheologial belief.
Regards, WM