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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 16:11:34 -0800
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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?

Fair enough?