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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: Thu, 7 Nov 2024 13:02:41 -0800
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On 11/6/2024 4:00 PM, Moebius wrote:
> Am 06.11.2024 um 21:59 schrieb Chris M. Thomasson:
>> On 11/6/2024 8:36 AM, WM wrote:
>>> On 05.11.2024 18:25, Jim Burns wrote:
>>>
>>>>
>>>>   Instead, there are boundary points.
>>>>   For each x not.in the intervals,
>>>>   each open set Oₓ which holds x
>>>>   holds points in the intervals and
>>>>   points not.in the intervals.
>>>> x is a boundary point.
>>>
>>> For every definable x we can decide whether it is inside the interval 
>>> including its endpoints or outside. No open intervals are necesseary 
>>> or useful. Your trick is cunning bot not accepted.
>>
>> For any z we can decide if its inside or outside of <whatever>
> 
> Hint: In contrast to WM's psychomath we do not have to "decide" if a 
> number z is inside or outside of a certain interval. It IS EITHER inside 
> of the interval OR NOT. (No "decision" necessary.)
> 

Indeed!