Enumerating the Rational Numbers
This Demonstration shows that the rational numbers are enumerable by visualizing the process of enumerating the fractions in a two-dimensional table. The process illustrates the fact that the Cartesian product of two enumerable sets is enumerable, as the positive rational numbers are a subset of . A nuance here is that many fractions of natural numbers represent the same rational number. With "repeat fractions" unchecked, only distinct rational numbers are enumerated.
 E. Maor, To Infinity and Beyond: A Cultural History of the Infinite, Princeton, NJ: Princeton University Press, 1991.