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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 10 Feb 2025 10:47:38 +0100
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On 09.02.2025 18:04, Richard Damon wrote:
> On 2/9/25 9:50 AM, WM wrote:
>> On 09.02.2025 14:08, Richard Damon wrote:
>>> On 2/9/25 5:46 AM, WM wrote:
>>>> On 08.02.2025 23:28, Richard Damon wrote:
>>>>> On 2/8/25 2:44 PM, WM wrote:
>>>>>> On 08.02.2025 12:51, Richard Damon wrote:
>>>>>>
>>>>>>> And thus you claim that 36 can not be factored, as all of its 
>>>>>>> factors are not needed.
>>>>>>
>>>>>> 1, 2, 3, 4, 6, 9, 12, 18, 36.
>>>>>> According to Cantor, the set of factors has a smallest element, 1, 
>>>>>> and the set of necessary factors has a smallest element, 6, or if 
>>>>>> double application is not allowed, 4.
>>>>
>>>>> And which of those was "necessary"?
>>>>>
>>>>> I don't need 6, because I can factor into 4 * 9
>>>>
>>>> 4 is not necessary because it is smaller than 6, and 6 is sufficient.
>>>
>>> But then your "necessary" has a application order, which the word 
>>> doesn't have.
>>
>> I apply Cantor's theorem B.
> 
> Do you mean axiom 8? I see nothing in his theorems that talk about 
> anything like this.

"Theorem B: Every embodiment of different numbers of the first and the 
second number class has a smallest number, a minimum."

Regards, WM