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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)
Date: Fri, 3 Jan 2025 12:35:06 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Fri, 03 Jan 2025 09:39:01 +0100 schrieb WM:
> On 02.01.2025 19:19, Jim Burns wrote:
>> On 1/2/2025 6:31 AM, WM wrote:
>>> On 31.12.2024 21:26, Jim Burns wrote:
>>>> On 12/31/2024 1:20 PM, WM wrote:
>> 
>>>>> Every union of FISONs which stay below a certain threshold stays
>>>>> below that threshold.
>>>>> Note: Every FISON stays below 1 % of ℕ.
>>>> For each finite ⟦0,j⦆, there are more.than.#⟦0,j⦆.many finite ⟦0,k⦆
>>> So it is for all definable natural numbers.
>> So it is for each finite.ordinal.
> That is impossible, because all finite ordinals can be subtracted from ℕ
> without infinitely many remaining. If you don't understand that, it is
> useless to go on.
>
>>> natural numbers which have only few successors because when they are
>>> removed nothing remains ℕ \ {1, 2, 3, ...} = { } .
>> ... the non.finite.ordinal natural.numbers.
>> We define natural.numbers to be only finite.ordinals, of which there
>> are more.than.any.finite.many.
> Infinitely many can be removed without remainder. But only finitely many
> can be defined by FISONs.
It is very obvious there are infinitely many FISONs.

-- 
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.