Re: The set of necessary FISONs

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:
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And thus you claim that 36 can not be factored, as all of its factors are not needed.

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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.

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And which of those was "necessary"?
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I don't need 6, because I can factor into 4 * 9

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4 is not necessary because it is smaller than 6, and 6 is sufficient.

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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.

 Regards, WM
 

Which tells us that no member of the set of FISONs is itself a necessary FISION in the set of FISONs we take as a union to make the Natural Numbers.
It says nothing about the Set of FISONs itself.
You just don't understand what the axioms talk about.