Consider the event in which you are asked to determine the sum of a number and 0. Do we want to perform the infinitude of cases that will demonstrate what each of these sums will be, or shall we implement the Scientific Method here? Just a reminder. The Scientific Method states that we: (1) Make an observation; (2) State a hypothesis; (3) Test our hypothesis; and (4) Either make a conclusion affirming the validity of our hypothesis, or amend the hypothesis and perform further tests, determining whether the amended hypothesis is true or needs to be further re-evaluated. Once we implement this approach, what do we determine? What were the advantages of this approach over the classic brute force approach we would have otherwise taken in the land of arithmetic? How can we further confirm the validity of our result? Suppose we now apply this new and improved approach to the situation of squaring a given value. What powerful conclusion can be made here, as a result of this more elegant analysis