Abstract

This paper mainly reconceives zero not as a mere absence but as an axis unifying positive and negative infinities. It introduces the notion of unzero (Ø) to emphasize zero’s active role in mathematical structure. By analysing limits of the form n/m as m→0⁺ and m→0⁻, it is shown that unzero naturally serves as a pivot between divergent magnitudes. The proposed work formalizes unzero within a minimal algebraic extension of the real numbers, compares it with projective and non‑standard frameworks, and explores illustrative examples in analysis and geometry. This unified perspective clarifies longstanding ambiguities around division by zero, offers a coherent notation respecting classical limits, and suggests avenues for further algebraic and topological development. 

Keywords

Critical thinking, Infinity, Projective geometry, Unzero, Zero.

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