A Detailed Note on Collatz-type Maps: Observation, a Simple Variant, and a Convergence Lemma

This note studies a simple version of the Collatz problem, a well-known question in mathematics about how numbers change when simple rules are repeatedly applied.
The paper shows that every number eventually reaches the number 1.
It also compares this simple map with the classic Collatz map, provides small examples and graphs, and suggests ideas for computational experiments.

This preprint is intended for educational and research purposes.
Author: Hana Abdelrahman, 15 years old.