On Logical Extension of Algebraic Division

Abstract

Basic arithmetic is the cornerstone of mathematics and computer sciences. In arithmetic, 'division by zero' is an undefined operation and any attempt at extending logic for algebraic division to incorporate division by zero has resulted in paradoxes and fallacies. However, there is no proven theorem or mathematical logic that suggests that, defining logic for division by zero would result in break-down of theory. Basing on this motivation, in this paper, we attempt at logically defining a solution for 'division by zero' problem.