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

On 1/2/25 6:40 AM, WM wrote:

On 01.01.2025 03:03, Richard Damon wrote:

On 12/31/24 1:05 PM, WM wrote:

 

Every mathematician knows that every FISON is finite as its name says and covers at most 1 % of ℕ.

>
But, when you actually take into accout EVERY FISON, the full INFINITE set, you get to them all

 Every union of FISONs including them all which stay below a certain threshold stays below that threshold. Every FISON stays below 1 % of ℕ.
What can't you understand?
 Regards. WM
 

No, becuase "all which stay below a certain threshol" is not EVERY FISON.
Again, you don't understand that the union of EVERY FISON is a infinite operation, since there are an infinite number of FISONs, even if each FISON is finite.
When you actually take the union of ALL that infinite set of FISONs, you will get the full infinite set of N.
You just don't understand that infinite is not finite, and you logic can't do that union of an infinite number of finite sets, as it tries to do them one by one, and never finishes.