Introduction to Set Theory is not a formal ETSU class (sadly). This would be a cross-listed 4000/5000 level class with potential catalog description: "Covers the standard topics of a first class in axiomatic set theory. Topics include equivalence relations, orderings, cardinalities and cardinal numbers, axiomatic development of the natural and real numbers, ordinal numbers, the Zermelo axioms of set theory, and the Axiom of Choice." The prerequisite is Mathematical Reasoning (MATH 3000). Introduction to Set Theory would be a prerequisite to the (graduate-only level) Set Theory class, for which I have online notes at Graduate Set Theory (these notes are still at the planning stage, as of Fall 2022).

Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of results which are particularly lengthy (shorter proofs are contained in the notes themselves). The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

1. Chapter 1. Sets.
2. Chapter 2. Relations, Functions, and Orderings.
3. Chapter 3. Natural Numbers.
4. Chapter 4. Finite and Countable Sets.
5. Chapter 5. Real Numbers.
6. Chapter 6. Cardinal Numbers.
7. Chapter 7. Ordinal Numbers.
8. Chapter 8. Alephs.
9. Chapter 9. The Axiom of Choice.
10. Chapter 10. Arithmetic of Cardinal Numbers.
11. Chapter 11. Uncountable Sets.
12. Chapter 12. The Axiomatic Set Theory.

Chapter 1. Sets.

• Section 1.1. Introduction to Sets. Section 1.1 notes
• Section 1.2. Properties. Section 1.2 notes
• Section 1.3. The Axioms. Section 1.3 notes
• Supplement. Proofs of Theorems in Section 1.3. Beamer file of Section 1.3 proofs of theorems
• Supplement. Printout of the Proofs of Theorems in Section 1.3. Print file of Section 1.3 proofs of theorems
• Section 1.4. Elementary Operations on Sets. Section 1.4 notes
• Supplement. Proofs of Theorems in Section 1.4. Beamer file of Section 1.4 proofs of theorems
• Supplement. Printout of the Proofs of Theorems in Section 1.4. Print file of Section 1.4 proofs of theorems
• Study Guide 1.

Chapter 2. Relations, Functions, and Orderings.

• Section 2.1. Ordered Pairs. Section 2.1 notes
• Supplement. Proofs of Theorems in Section 2.1. Beamer file of Section 2.1 proofs of theorems
• Supplement. Printout of the Proofs of Theorems in Section 2.1. Print file of Section 2.1 proofs of theorems
• Section 2.2. Relations. Section 2.2 notes
• Supplement. Proofs of Theorems in Section 2.2. Beamer file of Section 2.2 proofs of theorems
• Supplement. Printout of the Proofs of Theorems in Section 2.2. Print file of Section 2.2 proofs of theorems
• Section 2.3. Functions.
• Section 2.4. Equivalences and Partitions.
• Section 2.5. Orderings.
• Section 2.6. Operations and Structures.
• Study Guide 2.

Chapter 3. Natural Numbers.

• Section 3.1. Introduction to Natural Numbers.
• Section 3.2. Properties of Natural Numbers.
• Section 3.3. The Recursion Theorem.
• Section 3.4. Relations, Operations, and Structures Revisited.
• Study Guide 3.

Chapter 4. Finite and Countable Sets.

• Section 4.1. Cardinality of Sets.
• Section 4.2. Finite Sets.
• Section 4.3. Countable Sets.
• Section 4.4. Linear Orderings.
• Section 4.5. Uncountable Sets.
• Study Guide 4.

Chapter 5. Real Numbers.

• Section 5.1. Integers and Rational Numbers.
• Section 5.2. Real Numbers.
• Section 5.3. Topology of the Real Line.
• Study Guide 5.

Chapter 6. Cardinal Numbers.

• Section 6.1. Cardinal Arithmetic.
• Section 6.2. The Cardinality of the Continuum.
• Section 6.3. Sets of Real Numbers.
• Study Guide 6.

Chapter 7. Ordinal Numbers.

• Section 7.1. Well-Ordered Sets.
• Section 7.2. Ordinal Numbers.
• Section 7.3. The Axiom of Replacement.
• Section 7.4. Transfinite Induction and Recursion.
• Section 7.5. Ordinal Arithmetic.
• Study Guide 7.

Chapter 8. Alephs.

• Section 8.1. Initial Ordinals.
• Section 8.2. Addition and Multiplication of Alephs.
• Study Guide 8.

Chapter 9. The Axiom of Choice.

• Section 9.1. The Axiom of Choice and Its Equivalents.
• Section 9.2. The Use of the Axiom of Choice in Mathematics.
• Section 9.3. Sets of Real Numbers Revisted.
• Study Guide 9.

Chapter 10. Arithmetic of Cardinal Numbers.

• Section 10.1. Infinite Sums and Products of Cardinal Numbers.
• Section 10.2. Regular and Singular Cardinals.
• Section 10.3. Exponentiaion of Cardinals.
• Study Guide 10.

Chapter 11. Uncountable Sets.

• Section 11.1. Filters and Ideals.
• Section 11.2. Closed Unbounded and Stationary Sets.
• Section 11.3. The Measure Problem.
• Section 11.4. Large Cardinals.
• Study Guide 11.

Chapter 12. The Axiomatic Set Theory.

• Section 12.1. The Zermelo-Fraenkel Set Theory with Choice.
• Section 12.2. Consistency and Independence.
• Section 12.3. The Universe of Set Theory.
• Study Guide 12.

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