  Consider a finite positive integer. If it is even, divide it by 2, and if it
is odd, multiply it by 3 and add 1. This will give you a new integer. Following
the procedure for the new integer, you will receive another integer. Repeat the
steps, and after a few repetitions, you will finally reach 1. Collatz's
conjecture states that the final integer in the mentioned process will always
be 1, no matter what integer it starts with. Although the procedure of the
conjecture is easy to describe, its correctness has not yet been confirmed.
This article proves the conjecture by introducing a tree topology of it. Given
the proposed tree, we can prove that all integers converge to a unique root and
that there is only one cycle on the tree. We also see how every trajectory ends
in 1.
