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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Thu, 21 Nov 2024 01:20:08 +0100
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Am 21.11.2024 um 01:12 schrieb Chris M. Thomasson:
> On 11/20/2024 4:11 PM, Chris M. Thomasson wrote:
>> On 11/20/2024 4:10 PM, Chris M. Thomasson wrote:
>>> 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.
>>
>> say balanced condition is zero. So, with the single unit weight on the 
>> right, place a unit weight on the left. We got a balanced scale 
>> representing 1 - 1 - 0?
> 
> 1-1=0 DAMN
> TYPOS! GRRRR! Sorry Everybody! ;^o

lol

Keep cool, man.

Hey, we are cool, buddy! :-)

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