Consider the function f: {1,2,...} {1,2,...} defined by x f(x) = if x is even, 2 (3x+1 if x is odd. Given a positive integer m, we can define a sequence of numbers as follows: x0 = m, X = f(x0), x2 = f(x1), x3 = f(x2), .... (i.e., we apply the function f to x; to obtain the next term Xi+1). The Collatz Conjecture states that this sequence will eventually reach the number 1, no matter the value of the starting integer m. This conjecture has not been proven mathematically, but it has been tested for all positive integers m