Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

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,

 

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.

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