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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 20 Nov 2024 23:57:15 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 20 Nov 2024 19:37:20 +0100 schrieb WM:
> On 20.11.2024 19:12, joes wrote:
>> Am Wed, 20 Nov 2024 17:51:19 +0100 schrieb WM:
>>> 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"
>> You are once again lacking in precision:
> It was Cantor who said the above. There is no lack of precision.
You misunderstood him. I don't see anything about successors.

>> every natural is finite and thus countable.
> According to Cantor there is no number missing, let alone infinitely
> many.
Numbers "missing" is meaningless. What did you mean to say here?

> Set theory claims that all natural numbers can be counted to such
> that no successors remain. That is false.
Obviously. There is no end to the successors such that you are done
counting them after some finite number.

-- 
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.