Abstract
The algebra of sets defines the properties and laws of sets; the set-theoretic operations of union, intersection, and complementation; and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions and performing calculations, involving these operations and relations. The relation consisting of all ordered pairs is called the cartesian product. This chapter describes two types of elements called maximal element and minimal element. The natural numbers with their usual ordering are an example of an order-complete set. The rational numbers ordered by size are not order-complete; however, the real numbers are order-complete. A set with a linear ordering is called a chain. The family of subsets of a set, ordered by inclusion, is an example of a partially ordered set that is not a linearly ordered set.
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