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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Fri, 14 Mar 2025 23:10:11 +0100
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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