Iteralis Theory

Iteralis Theory is a mathematical framework that studies numbers through their behavior under repeated operations rather than their static properties. Instead of focusing only on what a number is, Iteralis Theory focuses on how a number evolves when a function is applied again and again. It introduces concepts such as growth product, convergence, divergence, and looping behavior to analyze whether a sequence stabilizes, cycles, or grows without bound. This theory is especially useful for understanding Collatz-type functions and other iterative systems, where long-term behavior cannot be seen from a single step. Iteralis Theory treats sequences as dynamic objects, revealing hidden structure in repetition and providing a systematic way to study motion, balance, and emergence within number systems.