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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Wed, 19 Mar 2025 10:39:38 +0100
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On 18.03.2025 21:40, joes wrote:
> Am Tue, 18 Mar 2025 16:34:21 +0100 schrieb WM:
>> On 18.03.2025 12:57, Alan Mackenzie wrote:
>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>
>>>> The set of FISONs is an inductive set. But it is not ℕ because ∀n ∈
>>>> UF: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>>
>>> That "because" doesn't hold
>>
>> Because you say so? That's not significant. Even if you can't understand
>> the correct argument, it is decisive: ℕ_def contains all numbers the
>> subtraction of which from ℕ does not result in the empty set. Obviously
>> the subtraction of all numbers which cannot empty ℕ cannot empty ℕ.
> There are many such sets: N\{0}, N\{1}, N\{2}, ...

ℕ_def contains only numbers with FISONs. N\{0} is not a FISON.

Regards, WM