A Proposal on the Equivalence of Infinitesimals and Imaginary Numbers via ...

Imaginary numbers are fundamentally operational within frameworks characterized by symmetry, micro-locality, and objectivity. The concept of the infinitesimal (differentiation) satisfies these three prerequisites: Symmetry: Represented by the convergence toward a value $a$ from both the infinitely positive (+) and negative (-) directions. Micro-locality: Defined by the limit approaching an infinitesimal point. Objectivity: Maintained through the rigorous definition of limits. Consequently, this hypothesis proposes that the mathematical mechanism of differentiation can be formally represented or executed through imaginary numbers.