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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 16 Jan 2025 19:37:39 -0500
Organization: i2pn2 (i2pn.org)
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On 1/16/25 8:28 AM, WM wrote:
> On 15.01.2025 23:31, Jim Burns wrote:
>> On 1/15/2025 1:17 PM, WM wrote:
>>> On 15.01.2025 16:16, Jim Burns wrote:
>>>> On 1/14/2025 4:07 AM, WM wrote:
>>
>>>>> Half are new.
>>>>
>>>> A step is never from finite to infinite.
>>>
>>> ∀n ∈ ℕ: 2n =/= n.
>>
>> A step is never from finite to infinite.
> 
> Then there is no complete set ℕ. Then new numbers can be inserted, which 
> are the result of doubling but have not been doubled.
> 
> Regards, WM
> 

No, it means your logic can't handle the complete set of N. No new 
numbers can be inserted, as if you HAD the complete infinity, they would 
all be there, the full *INFINITE* (and thus without end) set of them.

There wouldn't be new number to insert, as they would all have been 
there already.

The fact that you think more can be created, just means you never 
understood how to have all of them in the first place.

It may be true that with YOUR deficient logic, you can't have the 
complete set of Natural Numbers, but that isn't a flaw in the set of 
Natural Numbers, it is in your logic, which is just based on Naive 
assumptions that just blow it up when misused.