The Foundational Definition of Infinite-Dimensional Mathematics: Expansion of Trends and Contraction of Structures

This article aims to establish the true foundational definition for the theory of infinite-dimensional mathematics, completely breaking away from the framework of traditional linear mathematics (such as exponentiation, root extraction, and other abstract functions). By redefining <i>energy trends</i> (infinite large) and <i>structural trends</i> (infinite small), and presenting their bidirectional interaction, we propose a new cosmic description system characterized by dynamic equilibrium, self-correction, and intrinsic imperfection.