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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Forgotten to answer?
Date: Sun, 26 Jan 2025 10:56:33 +0100
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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