Re: The set of necessary FISONs

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.

>
The problem is your recursion on FISONs can't complete

 Try to understand Cantor's theorem.

I do, you don't.
Induction doesn't "build" a set, it test a set.
The other axioms are what build the set of Natural Numbers.
Your inabiiity to actually work with axioms, which you just call mathologies, makes it so you don't know what you are talking about.
Your induction proof shows that the set of FISONs has no necessary member, which means we can from the Naturals from the Union of a set of FISONs that can exclude any FISON, and in fact any finite set of FISONs.
The problem is the set you are trying to talk about, a set of FISONs that contain only FISONs that are necessary after removing all FISONs below then is a set that can't actually be defined in anything but the broken Naive Set Theory, and shows that you are just working in the Naive Mathematics based on Naive Logic, that has also been proven to be incorrect. That is the problem of trying to declaire the axiomization of Mathematics and Logic as a Mathology, it just leaves you with Naive Logic that is broken.
Sorry, you are just proving that you are nothibng but an ignorant crank that can say impresive words that you just don't know what they mean.

 Regards, WM