Abstract
This chapter focuses on ordered sets. A relation ϱ ⊂ X × X is said to be an ordering relation on the set X if it is reflexive, antisymmetric, and transitive. The set N of all natural numbers is ordered by the divisibility relation. If X is a finite set, then any relation that orders X can be described by reference to a geometrical illustration by means of diagrams. The chapter illustrates relations that order certain finite sets and presents a theorem that establishes a relationship between those relations that order a given set X and those relations that are irreflexive and transitive on X. The concept of maximal and minimal elements is further explained in the chapter. The chapter also presents examples that show that in an ordered set, there may be one or more maximal elements and even infinitely many such elements. However, there are ordered sets in which there are no maximal elements.
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