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

On 12/30/24 4:45 PM, WM wrote:

On 30.12.2024 21:10, joes wrote:

Am Sun, 29 Dec 2024 23:31:46 +0100 schrieb WM:

 

My theorem: Every union of FISONs which stay below a certain threshold
stays below that threshold.

Groundbreaking.

 And proven. My threshold is not a fixed number but a potentially infinite set which never grows to more than 1 % of ℕ. Proof: Every FISON that is multiplied by 100 remains a FISON that can be multiplied by 100 without changing this property.
 Regards, WM
 

No, your threshold is just an admission that you are only going to look at a finite set, and NOT the infinite set you want to talk about.'
All you have proved is that any finite set has a maximum value, while the INFINITE set of Natural Numbers (or FISONs) do not, and thus your logic can't talk about "all".
Sorry, you are just proving your stupidity.