An Introduction to Mathematical Analysis
for Economic Theory and Econometrics
Dean Corbae, Max Stinchcombe, and Juraj Zeman
December 2002, Modified May 27, 2003, March 31, 2004, June 2008
Contents1
Logic 1
1.1 Statements, Sets, Subsets, and Implication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Statements and Their Truth Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.a Ands/Ors/Nots as Intersections/Unions/Complements . . . . . . . . . . . . . . . . . . . 2
1.2.b Implies/Equivalence as Subset/Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.c The Empty Set and Vacuously True Statements . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.d Indicators and Ands/Ors/Nots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Proofs, a First Look . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Logical Quantifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Taxonomy of Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
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DedicationsTo my family: those who put up with me in the past - Josephine and Phil - and especially those who put up withme in the present - Margaret, Bethany, Paul, and Elena. D.C.To Rigo and Beth, who sometimes tolerated, sometimes encouraged, and sometimes rather disliked my absorp-tion with this project. M.B.S.To my family. J.Z.