Re: The set of necessary FISONs

On 2/10/25 10:00 AM, WM wrote:

On 10.02.2025 13:37, Richard Damon wrote:

On 2/10/25 4:56 AM, WM wrote:

 

The set of useless FISONs is inductive and therefore infinite. No FISON can change the assumption U(A(n)) = ℕ. Therefore every FISON can be omitted. ==> { } = ℕ.
>

Which means that each element is not needed, but doesn't prove that you can't get the answer from a union of an infinite set of them.

 Does Zermelo define a set by induction or only its elements?
 Regareds, WM
 

Zermelo BUILDS a set by creating its members. Note, you keep on confusing a property of the members for a property of the set.
No individual FISON is required to build a set of FISONs whose union is the set of Natural Numbers, but that doesn't mean the set of FISONs you CAN use is empty.
Just like no factor of 36 is REQUIRED to factor 36, but you can still use elements of the set of factors of 36 to factor 36 with.
Sorry, you are just proving your ignorance of what you talk about, because you reject the basics of logic.