Sujet : Re: The set of necessary FISONs
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 11. Feb 2025, 10:31:48
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vof5e4$1n7gr$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
User-Agent : Mozilla Thunderbird
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 or my book
W. Mückenheim: "Mathematik für die ersten Semester", 4th ed., De Gruyter, Berlin (2015)
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.
Either you accept both proofs or none. But without there is no set theory.
Regards, WM