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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sat, 14 Dec 2024 13:53:37 -0500
Organization: i2pn2 (i2pn.org)
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On 12/14/24 10:46 AM, WM wrote:
> On 14.12.2024 12:06, joes wrote:
>> Am Sat, 14 Dec 2024 09:42:37 +0100 schrieb WM:
>>> On 14.12.2024 09:30, Mikko wrote:
>>>> On 2024-12-13 10:28:44 +0000, WM said:
>>>>> On 13.12.2024 10:46, Mikko wrote:
>>>>>
>>>>>> Between any two intervals there is space and that space contains
>>>>>> other intervals.
>>>>> No. Starting from a point in the complement the cursor will hit a
>>>>> first interval. This is true for all visible intervals.
>>>> False. From a point that is not a part of an interval no interval is
>>>> the nearest one because another interval is nearer.
>>> IF ALL intervals and their endpoints are existing as invariable points
>>> on the real line this cannot happen. In potential infinity however
>>> between any two points new intervals come into being.
>> They are ALREADY there.
> 
> Therefore they cannot appear after the cursor has passed their 
> positions. Every interval and every end of an interval would be hit by 
> the cursor.
> 
> Regards, WM
> 
> 

Where did the cursor come from in the first place?

And why did it pass them when you tried to place t?

This is your old problem of there not being a "next" in a dense set.