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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Wed, 8 Jan 2025 22:57:52 +0100
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On 08.01.2025 21:07, Jim Burns wrote:
> On 1/8/2025 9:35 AM, WM wrote:
>> On 08.01.2025 12:04, FromTheRafters wrote:
>>> WM formulated on Wednesday :
> 
>>>> If ω exists, then ω-1 exists.
>>>
>>> Wrong.
>>
>> A set like ℕ has a fixed number of elements.
> 
> Yes.

|ℕ| is invariable. |ℕ| = |ℕ|/2 is wrong.

> Our sets do not change.
> Our set ℕ does not change.
> 
>> If ω-1 does not exist,
>> what is the fixed border of existence?
> 
> Membership in ℕ is determined by ℕ.rule.compliance,
> not by position relative to a border.element.
> 
> Each object complying with the ℕ.rule is in ℕ
> Each object not.complying is not.in ℕ

The rule is for n there is n+1. But the successor is not created but 
does exist. How far do successors reach? Why do they not reach to ω-1? 
Where do they cease before?
> 
> Compliance and non-compliance do not change.
> Membership does not change.

Then tell me if n = 7 exists and n = ω-1 does not exist where the border 
lies.
> 
> No element is the border.element
> because
> each element is smaller.than another, fuller element,
> and so, not on the border.

"And so on" can only happen, when the elements are created. Potential 
infinity.
> 
> Which elements are in ℕ doesn't change.

Then tell me if n = 7 exists and n = ω-1 does not exist where the border 
lies.

Regards, WM