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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 17 Dec 2024 11:30:46 +0100
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On 17.12.2024 00:57, Richard Damon wrote:
> On 12/16/24 3:59 AM, WM wrote:
>> On 15.12.2024 22:14, Richard Damon wrote:
>>> On 12/15/24 2:44 PM, WM wrote:
>>>> On 15.12.2024 13:54, Richard Damon wrote:
>>>>>
>>>>> You can't "name" your dark numbers,
>>>>
>>>> because they are dark.
>>
>>>> |ℕ \ {1, 2, 3, ...}| = 0 cannot be accomplished by visible numbers 
>>>> because ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>
>>> Which just shows that the full set in infinte, and any member in it 
>>> is finite, and not the last member.
>>
>> Many members can be subtracted individually but infinitely many 
>> members cannot be subtracted individually. They are belonging to the 
>> set. They are dark.

> Sure an infinite number of members can be subtracted individually,

An unbounded number can be subtracted individually. However, if all are 
subtracted individually, then a last one is subtracted. That cannot happen.

Regards, WM