A Reference Orbital Analysis of Grandi's Series

Abstract

A Reference Orbital Analysis of Grandi's Series Author: Dler Amin MohammedDate: 17 October 2026 This preprint presents a proposed mathematical interpretation of Grandi's series (1 - 1 + 1 - 1 + ...), based on the Reference Orbital System introduced by Dler Amin Mohammed. The study examines the distinction between a numerical value outside an infinite series and an element represented within an infinite reference system. The author proposes that operations involving elements of an infinite reference system should be examined according to the rules of that system. The paper questions the direct algebraic derivation of S = 1/2 from the divergent series and proposes a reference-based framework for further mathematical investigation. The ordinary sum of Grandi's series does not converge, while the value 1/2 is valid under certain generalized summation methods. This work presents a preliminary mathematical hypothesis requiring further formal definitions and proofs. Keywords: Grandi's Series, Reference Orbital System, Infinity, Divergent Series, Mathematical Foundations. © Dler Amin Mohammed — 2026