A note on the Collatz Conjecture

Take your favorite positive integer. If it's even, divide it by 2. If it's odd, multiply by 3 and add 1. Continue these steps with the new number you get and repeat forever. The Collatz conjecture claims that any positive integer you start with, you will eventually end up at 1. Recently, Terence Tao proved some strong partial results on this conjecture. In light of this, I will remark on some (not new) theorems involving this infamous conjecture.