Re: how

Le 22/06/2024 à 13:58, Jim Burns a écrit :

All of which is irrelevant to ⋃{}
which is always {}

"Theorem B: Every embodiment of different numbers of the first and the second number class has a smallest number, a minimum." [Cantor, p. 332]
The set of FISONs has a smallest element, {1}. The set of FISONs covering the first 100 natnumbers has a smallest element, namely {1, 2 3, ..., 100}. The set of FISONs covering the natural numbers has no first element. On the contrary we can prove that every FISON fails. Only a very fanatic matheologian like Franz Fritsche can claim, that the union of FISONs is infinitely larger than every FISON. According to Cantor's theorem B a set of necessary FISONs to be unioned does not exist.
Therefore we have: UF(n) = ℕ ⟹ U{ } = ℕ.
Regards, WM