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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 6 Nov 2024 19:22:40 +0100
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On 06.11.2024 12:46, Richard Damon wrote:
> On 11/5/24 7:34 AM, WM wrote:
>> On 05.11.2024 13:03, Richard Damon wrote:
>>> On 11/5/24 3:45 AM, WM wrote:
>>
>>>> I describe that a point between two finite intervals has two finite 
>>>> intervals around it. Even this simple conclusion must be denied by 
>>>> the believers in matheology.
>>
>>> If you mean that between to finite length intervals, which include 
>>> there endpoints, and a point that is between those two intervals, 
>>> then YES there exist two other intervals between the point and those 
>>> two intervals.
>>
>> These other intervals also have irrational endpoints. Every point 
>> outside of an interval is next to some endpoint which is irrational.
> 
> Or rational endpoints.

No, the rationals are centres of their intervals.
> 
> There is no "next to" on the dense line

Every positive point is nearer to zero than to any negative point.
Of -x and 0 the latter is next to any positive x.

Regards, WM