The Finite-Infinite Dialectic: A Mathematical and Physical Framework

This work formalizes the dialectical relationship between finite and infinite sys- tems through set theory, measure theory, and dynamical transformations. We pro- pose a framework where infinity is operationally defined via finite subsystems that ”convert” their complementary regions through mathematical transformations. Ap- plications to cosmology, quantum gravity, and string theory are explored, with experimentally testable predictions.