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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Thu, 20 Mar 2025 15:57:15 +0100
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On 20.03.2025 13:42, FromTheRafters wrote:
> WM explained :

>>
>> I did not prove that an infinite set is equal to an empty set. I 
>> proved that *if* the union of FISONs is ℕ, then ℕ is empty. That is 
>> far from what you think.
> 
> I think that you didn't 'prove' anything.

Then you cannot follow mathematical thought.

> Your notions, based on your 
> intuition alone,

They are based on induction alone:

Peano: 1 and if n then n+1.

Zermelo: { } and if a then {a}.

WM: ℕ \ {1} = ℵo and if ℕ \ {1, 2, 3, ..., n} = ℵo then ℕ \ {1, 2, 3, 
...., n+1} = ℵo.

The infinities defined by induction by these three derivations cannot be 
distinguished.

Regards, WM