Re: The set of necessary FISONs

WM brought next idea :

On 23.02.2025 23:03, Jim Burns wrote:

On 2/23/2025 2:32 PM, WM wrote:

On 23.02.2025 19:34, Jim Burns wrote:

On 2/23/2025 9:43 AM, WM wrote:

 

There is no reason to consider {{F}} at all.

>
There is reason, but
only for people wanting to be correct.

>
Peano, Zermelo, or v. Neumann

 ...agree that {{F}} ≠ {F}

>
and also that 3 ≠ pi.

 

Peano, Zermelo, or v. Neumann create ℕ

 Peano, Zermelo, and v. Neumann assert axioms
from which the existence of ℕ follows
in a finite.sequence of not.first.false claims.

>
These axioms can be applied to show that all FISONs can be removed.

Not in a system where sets don't change. You can envision a set containing FISONs you have chosen from the set of FISONs (a.k.a. the set of natural numbers) but if you choose none of them you get the empty set.
Nothing has been *removed* leaving your imaginary dark numbers behind.