Problem sets

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Include worked solutions (answer key)

§1 The Set ℕ of Natural Numbers (12)

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12

§2 The Set ℚ of Rational Numbers (8)

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

§3 The Set ℝ of Real Numbers (8)

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

§4 The Completeness Axiom (16)

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16

§5 The Symbols +∞ and −∞ (7)

5.1 5.2 5.3 5.4 5.5 5.6 5.7

§6 ★ A Development of ℝ (5)

6.1 6.2 6.3 6.4 6.5

§7 Limits of Sequences (5)

7.1 7.2 7.3 7.4 7.5

§8 A Discussion about Proofs (10)

8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10

§9 Limit Theorems for Sequences (18)

9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18

§10 Monotone Sequences and Cauchy Sequences (12)

10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12

§11 Subsequences (11)

11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11

§12 lim sup's and lim inf's (14)

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 12.14

§13 ★ Some Topological Concepts in Metric Spaces (15)

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 13.14 13.15

§14 Series (14)

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13 14.14

§15 Alternating Series and Integral Tests (8)

15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8

§16 ★ Decimal Expansions of Real Numbers (10)

16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10

§17 Continuous Functions (16)

17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 17.10 17.11 17.12 17.13 17.14 17.15 17.16

§18 Properties of Continuous Functions (12)

18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 18.10 18.11 18.12

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