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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Thu, 13 Mar 2025 10:15:25 +0100
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On 12.03.2025 23:13, FromTheRafters wrote:
> WM wrote :
>> On 12.03.2025 21:12, FromTheRafters wrote:
>>> WM wrote on 3/12/2025 :
>>>
>>>> Inductive sets do not contain dark numbers.
>>>
>>> Is the set of natural numbers an inductive set?
>>
>> The set of definable natural numbers
> 
> [...]
> 
> That is not what I asked.

Then you should specify what you ask.
The set of definable natural numbers is an inductive set.
Cantor's set ℕ of natural numbers contains but is not an inductive set.
Proof: If ℕ \ {1, 2, 3, ..., n} = ℵo, then ℕ \ {1, 2, 3, ..., n+1} = ℵo.

Regards, WM