Re: The set of necessary FISONs

On 22.01.2025 19:01, Python wrote:
 > Le 22/01/2025 à 16:04, WM a écrit :
 >> Assume UF(n) = ℕ. The small FISONs are not necessary. What is the first necessary FISON? There is none! All can be dropped. But according to Cantor's Theorem B, every non-empty set of different numbers of the first and the second number class has a smallest number, a minimum. This proves that the set of indices n of necessary F(n), by not having a first element, is empty.
 > Being "necessary" in an union of sets is not a property of a given element. It is a property of a subset.
Cantor's theorem concerns the set of indices n of FISONs F(n).
 > If you have three coins of 2 euros not a single one is "necessary" to pay a 3 euros drink
This failing analogy has been repeated again an again, first by Rennenkampff, because their authors do not understand the principle: Cantor's theorem concerns the set of indices or ordinal numbers, not a set of sets.
Therefore first you have to enumerate the euros or the sets {1, 2}, {2, 3}, {1, 3}. Then Cantor's theorem can be applied. In the given order the first necessary set is the second one.
Also in the case of coins the first one is not necessary.
Let me know whether you will be able to understand this simple explanation.
Regards, WM