A set, which should be thought of simply as a collection of objects, is called countable if it either consists of a finite number of objects or if the objects can be put in one to one correspondence with the integers. Two sets are defined to be of the same cardinality if the elements of one set can be mapped in a one to one fashion onto the elements of the second set. Thus infinite sets that are countable have the same cardinality as the integers. As a simple example, consider the set of even integers. Naively one might think that the set of even integers is somehow smaller than the set of all integers. However consider the function f(n) = n/2. This function exhibits a one-to-one mapping of the even integers onto all integers, proving that the set of even integers is countable. In a similar fashion...