Numerical Computations For Operator Axioms

TL;DR

This paper introduces numerical methods to approximate real numbers with base-b expansions, facilitating the application of new operator axioms in mathematical models for complex scientific rules.

Contribution

It presents a novel numerical computation approach for approximating real numbers using base-b expansions, extending operator axioms in mathematical modeling.

Findings

New numerical methods for real number approximation

Enhanced modeling of complex scientific rules

Potential applications in engineering computations

Abstract

The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new operators help to describe complex scientific rules which are difficult described by traditional equations and have an enormous application potential. As to the equations including new operators, engineering computation often need the approximate solutions reflecting an intuitive order relation and equivalence relation. However, the order relation and equivalence relation of real numbers are not as intuitive as those of base-b expansions. Thus, this paper introduces numerical computations to approximate all real numbers with base-b expansions.