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17. Index......Page 0 1.1 Set Language-A mathematical Shorthand......Page 2 1.2 Generalized Unions and Intersections; DeMorgan's Law......Page 7 1.3 The Russell Paradox*......Page 8 1.4 Cartesian Products and Functions......Page 9 1.5 The Inverse Function......Page 15 1.6 The Field of Rational Numbers......Page 21 1.7 Ordered Fields......Page 24 1.8 The Real Numbers as a Complete Ordered Field......Page 29 1.9 Properties of the Least Upper Bound......Page 33 1.10 Representations of the Real Numbers by Decimals*......Page 37 1.11 Existence and Uniqueness of a Complete Ordered Field*......Page 42 1.12 The Hierarchy of Numbers......Page 47 1.13 Cardinal Numbers......Page 49 1.14 The Cantor Set*......Page 56 2.15 Limit of a Sequence......Page 68 2.16 Three Fundamental Properties of Convergent Sequences......Page 71 2.17 Manipulation of Sequences......Page 73 2.18 Monotonic Sequences......Page 78 2.19 The Geometric Series......Page 80 2.20 The Number Line......Page 83 2.21 The Nested-Interval Property of R......Page 85 2.22 The Location of the Rationals and Irrationals Relative to the Reals......Page 88 2.23 Accumulation Point......Page 90 2.24 Limit of a Function......Page 93 2.25 Lim

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Author

Hans Sagan

Language

EN

Category

nonfiction

Subjects

Mathematics, Analysis, Stem