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

On 02.01.2025 19:53, Jim Burns wrote:

On 1/2/2025 6:35 AM, WM wrote:

On 01.01.2025 01:45, Jim Burns wrote:

On 12/31/2024 1:05 PM, WM wrote:

 

I don't stop
but know that
every FISON is finite as its name says
and covers at most 1 % of ℕ.
If you don't agree
find a counterexample.

>
No FISON is smaller than 1% of the maximum FISON.

>
{1} is smaller than {101} which is
smaller than all larger FISONs.

 ...larger FISONs _which exist_
something which frequently goes without saying.
 "Larger FISONs which exist" excludes
a maximum FISON.
How we know it's excluded is
NOT
because we can see all FISONs
but
because we can see a description of all FISONs,

 From this description we know that every FISON has
|ℕ \ {1, 2, 3, ..., n}| = ℵo
successors. Therefore it covers less than 1 ppb of ℕ.

A description of FISONs can be grasped.

Can you grasp the three lines above?
Regards, WM