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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 5 Jan 2025 12:18:18 +0100
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On 04.01.2025 23:30, Moebius wrote:
> Am 04.01.2025 um 21:38 schrieb Chris M. Thomasson:
>> On 1/4/2025 12:48 AM, WM wrote:
> 
>>> An interval of natural numbers without any prime number is called a 
>>> prime gap. The sequence of prime gaps assumes arbitrarily large 
>>> intervals but it cannot become actually infinite.
> 
> Yeah, it cannot "become" actually infinite because it already _is_ 
> infinite,

No term is infinite.
> 
>>> None of the numbers n! + 2, n! + 3, n! + 4, ..., n! + n can be prime 
>>> because n! = 123... n contains 2, 3, ..., n as factors already. 
>>> Therefore the set of gaps has no upper bound.
> 
> DAS stimmt sogar.

Na also.

> Eine Menge ist ENTWEDER endlich, ODER unendlich (=nicht endlich).
> 
> Eine andere Möglichkeit gibt es nicht.

Doch, sie kann nicht existieren: Menge der Kardinalzahlen.

Gruß, WM