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

On 12/29/24 5:39 AM, WM wrote:

On 28.12.2024 18:48, joes wrote:

Am Sat, 28 Dec 2024 17:50:49 +0100 schrieb WM:

 

A good example is the set of FISONs. Every FISON contains only a
negligible quantity of natural numbers. A generous estimation is: Every
FISON contains less than 1 % of all natural numbers. There is no FISON
that contains more than 1 %. Therefore the union of all FISONs contains
less than 1 % of all natural numbers. Outside of the union of FISONs are
almost all natural numbers.

A relative size is useless because it is still exactly as infinite,
i.e. countable.

 A relative size is very useful in order to correct the fantasy claim that the union of all FISONs covers the infinite gap between all FISONs and ω.
 Regards, WM

Except that for infinite sets, if they have a finite "ratio" they are the same size.
That is just one property of INFINITE sets, that you finite size logic can't handle with.
Sorry, you are just ADMITTING to your ignorance.