chapter  28
4 Pages

Least Upper Bound and Greatest Lower Bound

LEAST UPPER BOUND AND GREATEST LOWER BOUND

In Chapters 21 and 22 the concepts of upper bounds and lower bounds were considered for the particular posets (El , <) where < is the usual "less than or equal to" relation. In Chapter 27, generalizations of these concepts were investigated for any set A and any partial order relation on A. Likewise, in Chapters 21 and 22 the notions of least upper bound and greatest lower bound were considered for the particular poset (E1 , <). These concepts are now generalized for any partially ordered set. As before, the symbol < is sometimes used for the partial order relation. But < is NOT necessarily the ordinary "less than or equal to." At times the actual partial order relation will be used, e.g., C in (Paa, b,

C).