Re: The set of necessary FISONs

On 2/15/25 9:55 AM, WM wrote:

On 15.02.2025 14:40, Richard Damon wrote:
 

And since you build your claimed "set" by Naive Set theory, your sets are worthless.

 Zermelo constructs his set in modern set theory. Induction concerns the whole set. Compare Zermelo: "In order to secure the existence of infinite sets, we need the following axiom." [Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, S. 266] This is the axiom of infinity proved by induction. It ascertains the existence of an infinite set. It ascertains the set Z, Z_0 and the union of singletons ℕ.

Yes, he constructs the set of Natural Numbers based on modern set theory.
That you think that the axiom of infinite is proven by induction just shows that you don't understand how logic work.
Axioms are NOT PROVED, but taken as axioms. The mere fact you don't understand that demonstrates your ignorance of what you are talking about.
He might make a philosophical argument based on ideas that look a lot like induction that it should be true, but that isn't a proof.
If he could prove it, it wouldn't need to be an axiom, but would be one of the Theorems of the system.
Then we get to your set, the set of "Necessary FISONs", which you claim can be built on "modern set theory", when you don't show how to do so, but just show that you don't understand even the logic behind modern set theory.

>
The set you show is empty, is the set of FISONs that are individually not necessary.

 The remaining set should have at least one element. But it has none.
Further it would be silly to claim that replacing a smaller FISON is helpful after a larger FISON has been removed.

Maybe to your stupid mind, but it turns out that you can't actually express what you want in a valid logic system, because you are too stupid, and logic needs to find a purple two-horned unicorn.
Your "logic" is built from inconsistant assumptions and Naive logic that just blows your logic into smithereens of contraditions, taking your brain with it.

 Regards, WM