Скачать или смотреть Operational Depth: A Unified Iterative Framework for Arithmetic

This paper proposes Operational Depth, a unified framework that redefines arithmetic as a dynamic, iterative process rather than a collection of static facts. By centering operations around an identity element, the author demonstrates that multiplication and exponentiation are generative processes that build from an origin, while division and logarithms are reductive processes that return to one. This perspective organizes the hierarchy of math into levels of computational cost, where higher-order functions are simply repeated iterations of lower-order ones. The research further extends this logic to continuous domains using differential equations and provides an algorithmic definition for square roots based on operational symmetry. Ultimately, this approach bridges the gap between abstract algebra and the practical ways computer hardware executes calculations.