Re: Forgotten to answer?

On 25.01.2025 18:03, FromTheRafters wrote:

WM pretended :

On 22.01.2025 19:01, Python wrote:
>
 > 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.

 Then how are these 'Cantor's Theorem' ordinals contructed?

That can be done in an arbitrary way. For the above sets of euros or for {a, b}, {b, c}, {c, a} the first necessary is the second. For FISONs F(n) I use the index n. But we can attach the ordinals in an arbitrary way. There is no first necessary and no first sufficient either. All FISONs fail to complete the set ℕ if it is fixed and greater than all FISONs. The potentially infinite collection UF(n) however is obviously produced.
Regards, WM