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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Sat, 15 Mar 2025 11:26:14 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Fri, 14 Mar 2025 23:10:11 +0100 schrieb WM:
> 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.
This makes NO SENSE. You either mean N_def=N (no single removed number
makes the set empty *facepalm*) or N_def={} (subtracting everything
makes the set empty).

> Obviously the subtraction of all numbers which
> cannot empty ℕ cannot empty ℕ.
What? Is N_def finite? (don't come at me with "potential").

>> Wrong.  It is an "instantaneous" definition which completes N.
> Yes, of course. But ℕ_def is not completed by its definition.
wat

>> There are
>> not various stages of "N" which are in varying stages of completion.
> ℕ_def is never complete.
Then it is not a set. If it were, it would equal N.

>>> 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.
No. What's undefined doesn't exist. "Tending" is a property of a
sequence, not of individual numbers.

>> 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.
You got that wrong.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.