| viXra.org > Set Theory and Logic > viXra:2412.0005 |
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| viXra.org > Set Theory and Logic > viXra:2412.0005 |
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Set Theory and Logic |
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Authors: Theophilus Agama
This note formalizes and applies the emph{Principle of Structural Dependency}, which asserts that if the foundation of a mathematical structure ( B ) consists of another structure ( A ), then ( A ) cannot exhibit a property distinct from ( B ), while ( B ) may possess properties not shared by ( A ). We verify this principle and apply it systematically to reconstruct concise proofs of several classical theorems, including Cantor's theorem, the Fundamental Theorem of Algebra, the Jordan Curve Theorem, the Monotone Convergence Theorem, and the Pythagorean Theorem. These reconstructions emphasize the structural underpinnings of these results, offering a novel perspective and demonstrating how foundational relationships can simplify complicated proofs.
Comments: 3 Pages. This is a short note containing a novel principle for reconstructing proofs.
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[v1] 2024-12-02 21:40:58
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