mathematical preliminaries this presents mathematical notationbackgroundand techniques used throughout the book this material is provided primarily for review and reference you might wish to return to the relevant sections when you encounter unfamiliar notation or mathematical techniques in later section on estimating might be unfamiliar to many readers estimating is not mathematical techniquebut rather general engineering skill it is enormously useful to computer scientists doing design workbecause any proposed solution whose estimated resource requirements fall well outside the problem' resource constraints can be discarded immediately sets and relations the concept of set in the mathematical sense has wide application in computer science the notations and techniques of set theory are commonly used when describing and implementing algorithms because the abstractions associated with sets often help to clarify and simplify algorithm design set is collection of distinguishable members or elements the members are typically drawn from some larger population known as the base type each member of set is either primitive element of the base type or is set itself there is no concept of duplication in set each value from the base type is either in the set or not in the set for examplea set named might be the three integers and in this casep' members are and and the base type is integer figure shows the symbols commonly used to express sets and their relationships here are some examples of this notation in use first define two setsp and { } {