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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Sun, 29 Dec 2024 21:27:31 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 29 Dec 2024 11:39:22 +0100 schrieb WM:
> 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. You seem to think there are only finitely many naturals
>> and therefore FISes. Of course, if you only consider fin. many, you
>> don’t have all.
> 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.
There is no gap. 

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.