ABSTRACT
In mathematics, a relation is a quite general device for specifying some interaction between two sets. The theory of relations is part of the foundation for the theory of functions. Particularly important for us will be the theory of equivalence relations. In everyday conversation, the word "relation" is used to mean a number of different things ranging from the very personal to the political. But in mathematics the word has a very particular meaning. The idea of "relation" is the basis for our study of functions and a number of other sophisticated ideas. The idea of "equivalence relation" is one of the most universal in mathematics. It is used extensively in algebra and other subjects to make new mathematical constructs. Among the most interesting and useful relations are order relations. There are several different types of orderings, including partial orderings and total orderings. One of the most profound ideas of modern mathematics is Georg Cantor's theory of the infinite.
