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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 20 Nov 2024 16:10:27 -0800
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On 11/20/2024 3:57 PM, joes wrote:
> 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.
> 

A balanced scale with no weights on either side. Place a unit weight on 
the right side and say this equal to 0 + 1. Wrt unit weight...

? ;^) lol.