One of the primary features of mathematics is its transformation of the workings of nature into symbolic form. After systematically examining, manipulating and analyzing these abstract symbols, hopefully one may obtain a deeper understanding of the world. Perhaps the best example of this approach is the use of set theory. Created by Georg Cantor in the 1870s as an outgrowth of his study of the concept of infinity and transfinite numbers, set theory can be applied to a huge range of phenomena.

Sets are collections of things or ideas. A box of chocolates, a flock of geese, a pack of cards, and the collection of numbers 1 to 10 are all examples of sets. The things that make up a set are the members or elements of that set. Some things may be members of one set but not members of another. Describing the way set elements relate...