On the 3X + 1 problem

This thesis is a contribution to the continuously expanding field of knowledge on the 3X + 1 problem. The 3x + 1 problem involves the behavior of a function, known in the literature of Mathematics as the Collatz function, attributed to its original author, Lothar Collatz. By continually applying the function to its output, iterates are produced thus forming a sequence of positive integers called the Collatz sequence. The 3x + 1 problem states that for any initial positive integer, the number 1 is always included in the Collatz sequence.The researchers intended this thesis to be an exposition of the primary findings of The 3x + 1 Problem by Eric Roosendaal and 3n + 1 Problem by Jeffrey Lagarias. Moreover, the writers of this thesis found patterns that occur in the concepts defined by the said researchers.