Re: The non-existence of "dark numbers"

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.

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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.