Math 304: Constructing the Real Numbers†
نویسنده
چکیده
1 The Natural Numbers 1 1.1 The Peano Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Proof by induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Comparing integral systems . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Definition by Induction . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6 Ordering the natural numbers . . . . . . . . . . . . . . . . . . . . . . 15 1.7 Variations on induction . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.8 Well-ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.9 Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.10 The natural numbers and cardinality . . . . . . . . . . . . . . . . . . 24
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