Aarav's Foundational Structure of Infinity

Important!: the complete data and files could not be uploaded in the nomination form because of technical glitches and errors in the website the complete data and files are given in this depository: https://doi.org/10.5281/zenodo.16900853 This paper introduces a novel mathematical framework that redefines the behavior of undefined expressions and expands the boundaries of traditional number systems. This theory establishes a new class of numbers—which provides defined values for operations historically considered undefined, such as division by zero, the zeroth root, and indeterminate solutions in equations. The framework proposes original mathematical symbols, laws, and theorems to consistently address expressions like 0/0, ⁰√x, and equations with infinite or no solutions. It also offers a new definition and numerical representation for infinity. By introducing previously undefined quantities into a structured and logical system, it aims to resolve several longstanding problems in mathematics, forming the foundation of a new and extended mathematical universe.