Re: Forgotten to answer?

On 26.01.2025 14:04, FromTheRafters wrote:

After serious thinking WM wrote :

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?

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That can be done in an arbitrary way.

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Arbitrarily constructed ordinals? Tell me more!

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

 I see set manipulations but no ordinals at all, arbitrary or not.

The ordinals of necessary sets are 2 and 3. The first necessary ordinal is 2.
Regards, WM