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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 10 Jan 2025 17:38:34 +0100
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On 10.01.2025 14:05, joes wrote:
> Am Fri, 10 Jan 2025 11:38:49 +0100 schrieb WM:
>> On 10.01.2025 10:15, joes wrote:
>>> Am Thu, 09 Jan 2025 22:55:13 +0100 schrieb WM:
>>>> On 09.01.2025 21:17, joes wrote:
>>>>> Am Thu, 09 Jan 2025 19:25:19 +0100 schrieb WM:
>>>>
>>>>>> Losing all numbers but keeping infinitely many is impossible in
>>>>>> inclusion-monotonic sequences.
>>>>> This case doesn't occur.
>>>> Loss of all numbers is proven by the empty intersection.
>>>> Keeping infinitely many is poved by Fritsche.
>>> ...for different cases. There is no empty segment, each is infinite.
>> Without empty endsegment, not all numbers become indices.
> Not true; the sequence is infinite.

That requires that all natnumbers are indices. That requires that no 
natnumber remains as content.
> 
>> Note that bijections need all the indices. There is no limit accepted.
> An infinite bijection is not finite.

Nevertheless there is no limit, let alone an empty limit of a sequence 
of infinite sets.

Regards, WM