Mathematical Methods of Engineering Analysis

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Mathematical Methods of Engineering AnalysisErhan C inlarRobert J. VanderbeiFebruary 2, 2000ContentsSets and Functions11Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Subsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Set Operations . . . . . . . . . . . . . . . . . . . . . . . . .2Disjoint Sets . . . . . . . . . . . . . . . . . . . . . . . . . .3Products of Sets . . . . . . . . . . . . . . . . . . . . . . . .32Functions and Sequences . . . . . . . . . . . . . . . . . . . . . . . .4Injections, Surjections, Bijections . . . . . . . . . . . . . . .4Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . .53Countability.

2 SETS AND FUNCTIONS Subsets A set A is said to be a subset of a set B if every element of A is an element of B. We write A ⊂ B or B ⊃ A to indicate it and use expressions like A is contained in B,

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