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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: Sun, 15 Dec 2024 07:52:16 -0500
Organization: i2pn2 (i2pn.org)
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On 12/15/24 6:05 AM, WM wrote:
> On 15.12.2024 11:49, Mikko wrote:
>> On 2024-12-14 15:46:04 +0000, WM said:
>>
>>> On 14.12.2024 12:06, joes wrote:
> 
>>>> 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.
> 
> You believe that only afterwards the first interval comes into being?
> That is not the infinity used in set theory.
> 
> Regards, WM
> 

There is no "next", only before or after in dense sets.

Next is a property of directly indexed sets, like the naturals, which 
don't have a "last", even in complete actual infinity.