In the simplest sense, addition is a process of combining groups of things to form a new, larger group. Consider two baskets of apples: if apples are transferred from one basket into the other, a new bunch of apples is formed that is understood to be larger than either of the original two bunches. This process lead ancient peoples to create what is probably the earliest branch of mathematics, namely arithmetic. Eventually people abstracted from groups of objects (like bunches of apples) the concept of number that represents the quantity of objects in a particular group (i.e., five apples). In this process, the meaning of addition transformed from "combining groups of objects" to "combining the numbers associated with groups". Simply, the addition of numbers allowed for the counting of objects by increments greater than one. For instance, in order to add together two apples and three apples...