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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 18:04:10 -0500
Organization: Peripheral Visions
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WM explained on 11/20/2024 :
> On 20.11.2024 21:08, FromTheRafters wrote:
>> 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.
>
> "not a single one of this epitome has been forgotten" means not a single one 
> remaining, let alone more than one.

No it doesn't, it means the system used to list them is inherently 
unable to miss any.