General Mathematics

Identifying Natural Limits to Infinite Algebraic Singularities with Null Algebra

Authors: Robert S. Miller
Comments: 22 Pages. (Note by viXra Admin: Please cite and listed scientific references)

This paper introduces a framework which regularizes the classical algebraic singularity, using the essential hyperbola y=1/x to illustrate its application. Traditional, classical mathematics leaves the behavior at the origin for this function undefined due to divergence toward unachievable infinities. By using the transformational matrix defined in Null Algebra to map u=-1/y, the defined subspace of y, we may focus on a rate of information transfer implied by the function, as x→0. This is achieved by imposing a strict constraint upon dy/du which is required for any function y=f(x) and based upon chosen scale for the system defined by y=f(x). This shall show the singularity cannot actually be achieved due to natural self-limiting properties unique to a given function which emerge from Null Algebra, leaving a function, that is piecewise defined and continuous.
Category: General Mathematics