Numeristic Mathematics (英語) ペーパーバック – 2019/12/19
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This book consists of four documents on numeristics and equipoint analysis. Numeristics is a number-based foundational theory of mathematics. Equipoint analysis is a system of calculus based on numeristic principles.
The four documents in this book:
Numeristics: A number-based foundational theory of mathematics. Numeristics aims to establish a foundation for mathematics which: is easier, more elegant, more rigorous, more natural, and more useful; defines all operations; handles the infinite numerically; and is based on an ultimate unity. It includes infinite numbers, with procedures for calculating with them, and classes for handling multivalued expressions.
Equipoint analysis: A numeristic approach to calculus. A system of calculus and analysis using numeristic principles and an extended number system. It uses multiple levels of sensitivity to extend real and complex arithmetic and evaluate equality. It then defines derivatives and integrals solely in terms of elementary arithmetic operations in this extended arithmetic.
Divergent series: A numeristic approach. An alternative approach to the theory of divergent series using numeristic and equipoint principles. Infinite divergent series can generate some striking results but have been controversial for centuries. The standard approaches of limits and methods of summation have drawbacks which do not account for the full range of behavior of these series. A simpler approach is developed here, which better accounts for divergent series and their sums.
Repeating decimals: A numerisitic approach. Theorems and proofs about repeating decimals, and an extension of repeating decimals using numeristic principles.