86572 - 2 - A Second Course in Formal Languages and Automata Theory

A set is a collection of elements chosen from some domain. If S is a finite set, we use the notation |S| to denote the number of elements or cardinality of the set. The empty set is denoted by ∅. By A∪B (respectively A∩B, A− B) we mean the union of the two sets A and B (respectively intersection and set difference). The notation A means the complement of the set A with respect to some assumed universal set U ; that is, A = {x ∈ U : x ∈ A}. Finally, 2 denotes the power set, or set of all subsets, of A. Some special sets that we talk about includeN = {0, 1, 2, 3, . . .}, the natural numbers, and Z = {. . . ,−3,−2,−1, 0, 1, 2, 3, . . .}, the integers.