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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 6 Jan 2025 07:28:28 -0500
Organization: i2pn2 (i2pn.org)
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On 1/5/25 1:14 PM, WM wrote:
> On 05.01.2025 19:03, joes wrote:
>> Am Sun, 05 Jan 2025 12:14:47 +0100 schrieb WM:
>>> On 04.01.2025 21:38, Chris M. Thomasson wrote:
>>>
>>>> For me, there are infinitely many natural numbers, period... Do you
>>>> totally disagree?
>>> No. There are actually infinitely many natural numbers. All can be
>>> removed from ℕ, but only collectively ℕ \ {1, 2, 3, ...} = { }.
>>> It is impossible to remove the numbers individually ∀n ∈ ℕ_def: |ℕ \ {1,
>>> 2, 3, ..., n}| = ℵo.
>> Well yes, the size of N is itself not a natural number. Big surprise.
>>
> 
> ℕ cannot be covered by FISONs, neither by many nor by their union. If ℕ 
> could be covered by FISONs then one would be sufficient. But for all we 
> have: Extension by 100 is insufficient. Every union of FISONs which stay 
> below 1 % stays below 1 %.
> 
> 1 % is an abbreviation for: Extension by a factor of 100 does not cover ℕ.
> 
> Regards, WM
> 
> Regards, WM

Of course it can, but only by an INFINTE set of them, something your 
brain just is too stupid to comprehend.

Sorry, but all you are showing is what you are trying to disprove. That 
infinite numbers behave in ways that your "finite" logic can't handle, 
and that you are too stupid to understand that.