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Alexey Stakhov
Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
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Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science
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Chapter 1
Foundations of the Constructive (Algorithmic) Measurement Theory
1.1. The Evolution of the Concept of “Measurement” in Mathematics
1.2. Axioms of Eudoxus–Archimedes and Cantor
1.3. The Problem of Infinity in Mathematics
1.4. Criticism of the Cantor Theory of Infinite Sets
1.4.1. Infinitum Actu Non Datur
1.4.2. Criticism of Cantor’s theory of sets in 19th and early 20th centuries
1.4.3. Research by Alexander Zenkin
1.5. Constructive Approach to the Creation of the Mathematical Measurement Theory
1.6. The “Indicatory” Model of Measurement
1.6.1. The conceptions of the “indicatory” element (IE) and the “indicatory” model of measurement
1.7. The Concept of the Optimal Measurement Algorithm
1.8. Classical Measurement Algorithms
1.8.1. Counting algorithm
1.8.2. “Binary” algorithm
1.8.3. Readout algorithm
1.8.4. Restrictions S
1.9. Optimal (n, k, 0)-Algorithms
1.9.1. Recursion method
1.9.2. Synthesis of the optimal (n, k, 0)-algorithm
1.9.3. Special cases of the optimal (n, k, 0)-algorithm
1.9.4. Optimal (n, k, 0)-algorithms and positional numeral systems
1.10. Optimal (n, k, 1)-Algorithms Based on Arithmetic Square
1.10.1. Synthesis of the optimal (n, k, 1)-algorithm
1.10.2. Arithmetic square
1.10.3. Optimal (n, k, 1)-algorithm
1.10.4. An example of the optimal (n, k, 1)-algorithm
1.10.5. The extreme particular cases of the optimal (n, k, 1)-algorithm
1.10.6. The importance of the binomial algorithms for mathematics and computer science
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