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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 11 Feb 2025 11:16:31 +0100
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On 11.02.2025 01:48, Jim Burns wrote:
> On 2/10/2025 7:05 PM, Richard Damon wrote:
>> On 2/10/25 10:02 AM, WM wrote:
>>> On 10.02.2025 13:37, Richard Damon wrote:
>>>> On 2/10/25 4:47 AM, WM wrote:
> 
>>>>> "Theorem B:
>>>>> Every embodiment of different numbers of
>>>>> the first and the second number class has
>>>>> a smallest number, a minimum."
>>>
>>>> So, your "Set of Required FISONs" isn't
>>>> a set of the first or second class,
>>>> it is an empty set.
>>>
>>> So it is.
> 
>> Which just shows that
>> no particular FISON is needed.
>>
>> Doesn't mean that you can't use
>> a set of FISONs to make
>> the set of Natural Numbers.
> 
> Yes.

Then name the first FISON that must exist according to Cantor's theorem, 
see above.

> ⎛ If no FISON is required
> ⎜ then no FISON is possible.

That is not necessarily so. But if a FISON or set of FISONs is possible 
and not empty, then it has a first element. Find it. Overcome the result 
of induction, i.e., infinity.

Regards, WM