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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Tue, 07 Jan 2025 04:40:54 -0500
Organization: Peripheral Visions
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WM has brought this to us :
> On 06.01.2025 23:43, Jim Burns wrote:
>> On 1/5/2025 1:14 PM, WM wrote:
>
>>> 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.
>> 
>> ℕ is the set of finite.ordinals.
>> ℕ holds each finite ordinal.
>> ℕ holds only finite.ordinals.
>
>>ℕ| is by definition the smallest transfinite number, larger than every
> natural number by every visible factor.
>> 
>> k ∈ ℕ  ⇒  k+1 ∈ ℕ
>> is true for both the darkᵂᴹ and the visibleᵂᴹ.
>
> One exception exists: ω-1.

Which remains undefined.