Re: The set of necessary FISONs

Am Tue, 11 Feb 2025 10:31:48 +0100 schrieb WM:

On 10.02.2025 16:16, Jim Burns wrote:

On 2/10/2025 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.

 
Do you accept ∀ᴺj′:∀ᴺi′:∃ᴺk′:
  k′ = max{i′,j′+1}
?

 
No, I won't try to dive into your private notation. How induction works
is well known. If not consult Wikipedia.
The set F of FISONs which can be removed without changing the assumed
result UF = ℕ is the infinite set F of all FISONs. This is proven by
just the same induction as Zermelo proves his infinite set Z.

Nope, any *finite* set of FISONs can be removed. The set of *those*
is infinite, but no set of removable FISONs is.
(Zermelo or whoever don’t prove the membership of infinite elements.)

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.