Zero Centric Arithmetic: Rethinking Division by Zero (Derna Academy Journal for Applied Sciences, 2025)
Abstracts are This paper redefines the concept of division by zero, a long-standing controversy in mathematics. In traditional field theory, division is defined as multiplication by the inverse, and since zero has no inverse, division by zero is treated as an exception and labeled "undefined." This approach, however, creates contradictions and confusion, especially when ad-hoc definitions such as are introduced.The paper proposes a new framework called Zero-Centric Arithmetic: Rethinking Division by Zero which interprets division as distribution. If the divisor is zero, there are no groups to distribute into, meaning the operation itself does not exist, rather than being undefined.This perspective treats zero not as a deficient element but as the central element of the number system, removing philosophical and educational ambiguities. Through practical examples (gift distribution, line slopes in geometry, limits in calculus), the paper demonstrates that interpreting division by zero as a non-existent operation is more consistent and intuitive.