On Logical Extension of Algebraic Division

TL;DR

This paper explores the possibility of logically defining division by zero, challenging traditional views and aiming to resolve paradoxes associated with extending algebraic division.

Contribution

It proposes a novel logical framework for division by zero, aiming to resolve longstanding paradoxes without breaking existing mathematical theories.

Findings

Proposes a logical extension for division by zero

Addresses paradoxes in algebraic division

Suggests potential for consistent extension of arithmetic logic

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.