ABSTRACT

The mathematical notion of order is an abstraction of the notion of dominance as expressed in such statements as “5 > 4,” “A c B,” “c comes before d,” “x is closer than y ,” . . .

We shall find two classes of configurations which express this concept. After verifying this fact, we shall give the final definition in a way that recognizes both alternatives. The remainder of the chapter will be devoted to defining a number of terms associated with ordered sets and developing a few of their properties.