REAL ANALYSIS with ECONOMIC APPLICATIONS . mathematics is very much like poetry . what makes a good poem - a great poem - is that there is a large amount of thought expressed in very few words. In this sense formulas like eπi + 1 = 0 are poems. Preface Chapter A Preliminaries of Real Analysis Elements of Set Theory | REAL ANALYSIS with ECONOMIC APPLICATIONS EFE A. OK New York University December 2005 . mathematics is very much like poetry . what makes a good poem - a great poem - is that there is a large amount of thought expressed in very few words. In this sense formulas like eni 1 0 or Zœ -œ e x dx y n are poems. Lipman Bers ii Contents Preface Chapter A Preliminaries of Real Analysis Elements of Set Theory 1 Sets 2 Relations 3 Equivalence Relations 4 Order Relations 5 Functions 6 Sequences Vectors and Matrices 7 A Glimpse of Advanced Set Theory The Axiom of Choice Real Numbers 1 Ordered Fields 2 Natural Numbers Integers and Rationals 3 Real Numbers 4 Intervals and R Real Sequences 1 Convergent Sequences 2 Monotonic Sequences 3 Subsequential Limits 4 Infinite Series 5 Rearrangements of Infinite Series 6 Infinite Products A. 4 Real Functions 1 Basic Definitions 2 Limits Continuity and Differentiation 3 Riemann Integration 4 Exponential Logarithmic and Trigonometric Functions 5 Concave and Convex Functions 6 Quasiconcave and Quasiconvex Functions Chapter B Countability B. 1 Countable and Uncountable Sets Losets and Q Some More Advanced Theory 1 The Cardinality Ordering 2 The Well Ordering Principle .
