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

On 29.12.2024 15:43, joes wrote:

Am Sun, 29 Dec 2024 12:05:26 +0100 schrieb WM:

On 28.12.2024 20:35, joes wrote:

Am Sat, 28 Dec 2024 14:58:50 +0100 schrieb WM:

 

Therefore the union of all of them contains less than half of all
natural numbers.

Worng.

My theorem: If all definable numbers (FISONs) stay below a certain
threshold, then every union of those FISONs stays below that
threshold.

The infinite union doesn’t.

The union of all FISONs below a certain threshold, namely a threshold
between which and ω there exist ℵ₀ natnumbers, remains below this very
threshold.