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From: Alan Mackenzie <acm@muc.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Tue, 18 Mar 2025 12:18:27 -0000 (UTC)
Organization: muc.de e.V.
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WM <wolfgang.mueckenheim@tha.de> wrote:
> On 18.03.2025 10:56, FromTheRafters wrote:
>> on 3/18/2025, WM supposed :

>>> The set is ordered and if it is actually infinite, then all its=20
>>> elements are there and=C2=A0 do not appear from nothing but then it h=
as a=20
>>> greatest element.

>> Nope, it is a limit ordinal.

> All elements of =E2=84=95 are there. That is the assumption. If no grea=
test can=20
> be identified, then the reason are dark numbers.

No, the reason is that there is no greatest element.  "Dark numbers" do
not exist, as has been proven in this thread.

> Otherwise only potential infinity could solve the dilemma.

There is no dilemma here.

"Potential infinity" doesn't exist in modern mathematics.  It was a
blind alley the pioneers of set theory drove up.  "Potential infinity"
isn't a useful concept and isn't needed in mathematics.

> Regards, WM

--=20
Alan Mackenzie (Nuremberg, Germany).