A Formal Solution to the Collatz Problem Based on Mixed Infinite Convergence Functions

This project presents a formal solution to the Collatz problem, one of the most iconic unsolved questions in mathematics, by introducing the framework of Mixed Infinite Convergence Functions. The central theorem (or postulate) is derived strictly from classical mathematical axioms: well-definedness, determinism, comparability, and infinite iterability. By applying this framework, the Collatz process is shown to be a specific instance whose convergence is formally confirmed as a direct consequence of the stated axioms. The document provides both the rigorous mathematical formalization and illustrative examples, demonstrating that every positive integer under the Collatz process inevitably reaches 1. This work elevates Collatz’s conjecture from an empirical observation to an axiomatic result and offers a new paradigm for the study of iterative discrete processes.