A Deep Study on Limit Theory: Mathematical Foundations, Computational Methods, MHD Heat Transfer, and AI Convergence Dynamics

The theory of limits forms the foundational basis for continuity, convergence, and stability in mathematical analysis. This paper provides an integrated study of limit theory, spanning its historical evolution, formal epsilon–delta structure, computational interpretations, and its broad applications across magnetohydrodynamic (MHD) heat transfer and artificial intelligence. Limit-based reasoning governs the behavior of numerical approximations, boundary-layer asymptotics in conductive fluid flows, and convergence dynamics in optimization and neural network learning. By uniting theoretical analysis with computational and physical applications, this study demonstrates the universal role of limits in shaping modern mathematics, engineering, and intelligent systems.