complete_numbers

Simple library to test the arithmetical properties of a number system allowing for zero division

All of the sets of numbers in general use (the natural, rational, real, and complex numbers) are limited because they not closed with respect to division--that is, there are input values to the division operation with no defined answer. This package is an experimental attempt to emulate the extension of the real numbers to the complex numbers. In the complex numbers, all numbers are of the form a+bi where i is defined as i^2 = -1. This experimental system seeks to extend the complex numbers by creating a system of numbers of the form a+bi+cphi+dpsi where i is defined as above, phi is defined as 1/0, and psi is defined as i/0.

If a consistent system can be created, it could allow for a mathematical space where all functions are both continuous and smoothly differentiable, eliminating singularities and potentially providing a valuable mathematical tool with potential applications in theoretical physics.