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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Mon, 02 Dec 2024 06:53:14 -0500
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Chris M. Thomasson brought next idea :
> On 11/30/2024 3:12 AM, WM wrote:
>> On 30.11.2024 11:57, FromTheRafters wrote:
>>> WM explained :
>>>> On 29.11.2024 22:50, FromTheRafters wrote:
>>>>> WM wrote on 11/29/2024 :
>>>>
>>>>>> The size of the intersection remains infinite as long as all 
>>>>>> endsegments remain infinite (= as long as only infinite endsegments are 
>>>>>> considered).
>>>>>
>>>>> Endsegments are defined as infinite,
>>>>
>>>> Endsegments are defined as endsegments. They have been defined by myself 
>>>> many years ago.
>>>
>>> As what is left after not considering a finite initial segment in your new 
>>> set and considering only the tail of the sequence.
>> 
>> Not quite but roughly. The precise definitions are:
>> Finite initial segment F(n) = {1, 2, 3, ..., n}.
>
> Finite? Huh? The natural numbers don't stop at n! WTF!!!!  Lay off the drugs.

That ordered set has a first element namely '1' and a last element, 
namely 'n' so yes, it is finite.

>> Endsegment E(n) = {n, n+1, n+2, ...}

This is his definition of endsegment, which as almost anyone can see, 
has no last element, so yes it is infinite. He says 'infinite 
endsegment' as if there were a choice, only to add confusion.