Re: Forgotten to answer?

On 26.01.2025 10:08, FromTheRafters wrote:

WM wrote :

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.

 Arbitrarily constructed ordinals? Tell me more!

Which of {a, b}, {b, c}, {c, a} are required  for the union {a, b, c}?
Indexing: 1. {a, b}, 2. {b, c}, 3. {c, a}.
The first set is not required because
{a, b, c} = {a, b} U {b, c} U {c, a} = {b, c} U {c, a}.
The second set is the first required one because
{a, b, c} = {b, c} U {c, a} =/= {c, a}.
Therefore Cantors's theorem supplies the set of ordinals {2, 3}.
By the way, every other choice of indices would yield the same Cantor-set {2, 3}.
Regards, WM