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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 15 Dec 2024 12:49:21 +0200
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On 2024-12-14 15:46:04 +0000, WM said:

> 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.

Yes, but not before another interval hits the cursor.

-- 
Mikko