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282(2): ◆Ph05QxAcng 2024/03/09(土) 19:38:56.00 ID:P9QGsLiu(14/21)調 AAS
論文の内容は以下のようになります
タイトル
A mathematical proof that existence is a silhouette
Abstract
I prove that existence is a silhouette.
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.
283: ◆Ph05QxAcng 2024/03/09(土) 19:39:11.26 ID:P9QGsLiu(15/21)調 AAS
>>282
Next, we demonstrate that the existence of A and A having elements in space are equivalent.
Suppose there exists an entity A that exists but does not have elements in space.
Consider A and its power set {A}.
If we assume that {A} also does not have elements in space,
and define B as a set of entities that do not have elements in space. Considering {B}, if {B} is assumed to not have elements in space, then B⊇{B} and {B}⊇B would mean B and {B} coincide. However, this contradicts Lemma 1.1.
Therefore, {B} is an element of space. Thus, by Lemma 1.2, both A and {A} are shown to be elements of space, which contradicts the premise.
Hence, {A} is an element of space.
Furthermore, from Lemma 1.2, it can be deduced that A is also an element of space.
Therefore, if A exists, it is shown that A has elements in space.
Since it is self-evident that having elements in space implies existence, it is demonstrated that existence and having elements in space are equivalent. Furthermore, having elements in space is equivalent to having a contour, thus existing is equivalent to having a silhouette.
284: ◆Ph05QxAcng 2024/03/09(土) 19:45:51.79 ID:P9QGsLiu(16/21)調 AAS
>>282
これもSakura Tachibanaの名前でサブミットしました
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