ミレニアム懸賞問題 (635ﾚｽ)
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285(1): ◆Ph05QxAcng [] 2024/03/09(土)19:55 ID:P9QGsLiu(17/21)
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タイトル
Request for Review of a Mathematical Proof: existence is a silhouette

内容
Dear Professor ***************,
I hope this email finds you well. My name is Sakura Tachibana.

I have recently completed a proof regarding that existence is a silhouette. I was wondering if you would be willing to review my proof.
The main ideas and conclusions of the proof are as follows:
existence is a silhouette.

For the complete proof, please refer to the attached PDF file and text.

I understand that you have a busy schedule, but if you could find the time to review my proof, I would be incredibly grateful. I am eager to improve my proof based on any feedback you may provide.

Thank you for considering my request. I appreciate your time and expertise.

Best regards,
Sakura Tachibana

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286(1): ◆Ph05QxAcng [] 2024/03/09(土)19:56 ID:P9QGsLiu(18/21)
>>285

Theorem
Existence is a silhouette.
Proof
First, we will demonstrate two lemmas.

Lemma 1.1: Consider an element 'a' and its power set {a}. These two are different entities.
Proof
Assume they are the same.
If there exist elements a, b, then the set {a, b} would be the same entity. The latter is seen as a single entity consisting of a and b, which are clearly different. Thus, the initial premise is contradicted, proving the lemma.

Lemma 1.2: Elements of a set that are elements of space are themselves elements of space.
Proof
Let a set be E, and suppose an element e of E is not an element of space. If E∩e = e, then despite e being a part of E, there would exist a part that is not an element of space, which is a contradiction. Therefore, the lemma is proven.

Taking the contrapositive, we obtain the following corollary.

Corollary 1.2.1: A set composed of elements that are not elements of space is not an element of space.

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