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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: Sun, 15 Dec 2024 16:13:55 -0500
Organization: i2pn2 (i2pn.org)
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On 12/15/24 1:57 PM, WM wrote:
> On 15.12.2024 13:52, Richard Damon wrote:
>> On 12/15/24 7:00 AM, WM wrote:
>>> On 14.12.2024 23:04, Jim Burns wrote:
> 
>>>> If ψ is finite, then ψ+1 is finite.
>>>> If ψ+1 is finite, then ψ+2 is finite.
>>>
>>> Yes, that is the potentially infinite collection of definable 
>>> numbers. But it explains nothing.
>>
>> That is the collection of numbers known as the Natural Numbers, so I 
>> guess you are admitting that your "Definable Numbers" include *ALL* of 
>> the Natural Numbers
> 
> Dark numbers are required to empty ℕ by |ℕ \ {1, 2, 3, ...}| = 0. All 
> definable numbers fail: ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> 
> Regards, WM
> 

And why do you need to do that?

All you are doing is showing that you don't understand that an infinite 
set doesn't have a "last" member, and is catagorically bigger than any 
finite set.

Thus, all you have done is shown that your logic is just totally 
exploded leaving a "dark hole" behind from its nuclear explosion into 
smithereens from the contradictions you make it generate.

Sorry, but that is the truth, which seems to be beyond your ability to 
understand.