We define the Collatz Function F_col:N->N(n) as follows: F_col(n):= n/2 if n is even, and F_col(n):= 3n+1 if n is odd We define the two branches f:N->N and g:N->N of the above function as follows: f(n):= n/2 if n is even and g(n):= 3n+1 if n is odd Also, we define the 'functional sequence' of a number n as the set of functions applied consecutively on n (obeying the obtained parities), and show that any two g's in a functional sequence must be separated by at least one f. Next, we prove that all numbers n, under repetitive execution of the Collatz function, eventually yield a certain E < n. This is obvious for even n values, since- F_col(n) = n/2 < n for even n For odd n values, we prove that any odd number n which does not yield an E < n under repetitive execution of the Collatz function, must possess a functional sequence of the form- S={gfgfgfgfgfgf...} We then prove that the existence of a number possessing such a functional sequence is not possible, implying that our statement is true for odd numbers as well. Hence, it follows that any natural number n, under repetitive execution of the Collatz function, must yield an E < n. The truth of the Collatz Conjecture follows immediately from the above.