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.
