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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 20 Nov 2024 15:08:58 -0500
Organization: Peripheral Visions
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WM was thinking very hard :
> On 20.11.2024 15:15, FromTheRafters wrote:
>> WM explained on 11/20/2024 :
>>> set theory claims that all natural numbers can be counted to such that no 
>>> successors remain.
>> 
>> No it doesn't.
>
> Even all rationals and algebraics.
>
> "we get the epitome (ω) of all real algebraic numbers [...] and with respect 
> to this order we can talk about the nth algebraic number where not a single 
> one of this epitome has been forgotten"
> "The infinite sequence thus defined has the peculiar property to contain the 
> positive rational numbers completely, and each of them only once at a 
> determined place"

Which doesn't support your claim at all. No mention whatsoever of no 
successors remaining.