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

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