Reinterpreting Multiplication by Zero and Zero Exponentiation
Keywords:
Zero-Centric Arithmetic, Multiplication by Zero, Zero Exponentiation, Double Absence, Undefined Operations, Arithmetic Foundations, Algebraic Consistency, Mathematical PhilosophyAbstract
This paper revisits the conventional rules governing multiplication by zero and the use of zero as an exponent. While the standard framework asserts fixed outcomes for these cases, such definitions have long raised both philosophical and educational questions. The work proposes a new perspective: treating multiplication by zero as the absence of any operation, and zero as an exponent as a stabilizing condition that preserves consistency in repeated multiplication. The unique case where both the base and exponent are zero is interpreted as the convergence of two distinct absences absence of quantity and absence of repetition highlighting its conceptual significance.
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