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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
 (extra-ordinary)
Date: Mon, 2 Dec 2024 15:56:39 -0800
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On 12/2/2024 3:53 AM, FromTheRafters wrote:
> 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.

I was thinking that WM thinks that n is a magical largest natural 
number. { 1, 2, 3, ... } = the_set_of_all_natural_numbers

Not showing an end point for it ala n. I got confused.


> 
>>> 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.