Zero Centric Arithmetic: Rethinking Division by Zero

• Omar Zargelin

  Office of Innovation and Entrepreneurship Projects, Libyan Authority for Scientific Research, Tripoli Libya

  Author

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.

1. Omar Zargelin, Office of Innovation and Entrepreneurship Projects, Libyan Authority for Scientific Research, Tripoli Libya

   مكتب مشاريع الابتكار وريادة الأعمال، الهيئة الليبية للبحث العلمي، طرابلس ليبيا

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