Algebra

A Symmetry-Based Proof of Commutativity, Order Dependence, and the Zero Product Property

Authors: Ibrahim Mutebi
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper presents an original proof of the commutative property for addition and multiplication using symmetric term interpretation and the fundamental ambiguity of sequential operations. Unlike traditional approaches that rely on induction or axioms, this method demonstrates how commutativity naturally emerges from the freedom to associate terms in algebraic expressions. The paper further examines subtraction and division, showing why they are not commutative, and explains the zero product property using clear mathematical examples and verbal reasoning. This approach is intended to provide both conceptual insight and pedagogical value, particularly for learners exploring the foundational properties of arithmetic.
Category: Algebra