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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Thu, 13 Mar 2025 11:37:53 +0100
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On 12.03.2025 23:06, Moebius wrote:
> Am 12.03.2025 um 22:31 schrieb Alan Mackenzie:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
> 
>>> If you were able to learn, then you would have the chance here:
>>> ℕ \ {1} = ℵo
>>
>> Where do you get that from?  You're trying to say a subset of N is
>> identical to the first transfinite cardinal.  That cannot be true.
> 
> Should read: |ℕ \ {1}| = ℵo

Yes, thank you.
> 
>>> and if ℕ \ {1, 2, 3, ..., n} = ℵo>> then ℕ \ {1, 2, 3, ..., n+1} = ℵo.
>>
>> Where do you get that from?  It is clearly false - the first of these
>> sets contains an element, n+1, that the second one doesn't.  Therefore
>> they are distinct sets.
> 
> Should read: and if |ℕ \ {1, 2, 3, ..., n}| = ℵo then |ℕ \ {1, 2, 3, 
> ..., n+1}| = ℵo.
> 
>>> Induction cannot cover all natural numbers but only less than remain
>>> uncovered.
> 
Try to find a defined FISON that can accomplish the same as the dark 
numbers do collectively, namely
ℕ \ {1, 2, 3, ...} = { }.

Regards, WM