Introduction

Problem list

Chapter 1: Sets

Hrbacek 1.1: Introduction to Sets

Hrbacek 1.2: Properties

Hrbacek 1.3: The Axioms

3.1
3.2
3.3
3.4
3.5
3.6
3.7

Hrbacek 1.4: Elementary Operations on Sets

4.3ab (so the manipulations in Velleman are justified by axiom now)
4.4
4.5
4.6

Chapter 2: Relations, Functions and Orderings

Hrbacek 2.1: Ordered Pairs

1.1
1.2
1.4
1.5

Hrbacek 2.2: Relations

2.1
2.2
2.3
2.4
2.6
2.7

Hrbacek 2.3: Functions

3.4
3.5
3.6
3.8
3.9
3.10
3.11
3.12
3.13

Hrbacek 2.4: Equivalence and Partitions

4.2

Hrbacek 2.5: Orderings

5.3
5.5
5.6
5.9
5.11
5.12
5.13
5.14

Chapter 3: Natural Numbers

Hrbacek 3.1: Introduction to Natural Numbers

1.1

Hrbacek 3.2: Properties of Natural Numbers

2.1
2.2
2.3
2.4
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13

Hrbacek 3.3: The Recursion Theorem

3.1
3.2
3.4
3.5
3.6

Hrbacek 3.4: Arithmetic of Natural Numbers

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9

Hrbacek 3.5: Operations and Structures

5.1
5.4
5.10
5.12

Chapter 4: Finite, countable and uncountable sets

Hrbacek 4.1: Cardinality of Sets (feel free to copy proofs of Velleman if necessary)

1.1
1.3
1.4
1.5
1.6
1.7

Hrbacek 4.2: Finite Sets

2.1
2.2
2.3
2.4
2.7

Hrbacek 4.3: Countable Sets

3.2
3.3
3.4
3.5
3.6
3.10

Hrbacek 4.4: Linear Orderings

4.1
4.2
4.3
4.8
4.10
4.11
4.12

Hrbacek 4.5: Complete Linear Orderings

5.2
5.4

Hrbacek 4.6: Uncountable Sets

6.1
6.2