"Naive Set Theory Notes" Webpage

Naive Set Theory Notes
Naive Set Theory, by Paul Halmos
(Princeton: D. Van Nostrand Company, 1960), reprinted by Dover Publications (2017). Halmos' Naive Set Theorem Van Nostrand version

Halmos' Naive Set Theorem Van Nostrand version

"Naive Set Theory" is not an official ETSU class. This would be a 3000 level class with potential catalog description: "Gives a introduction set theory covering topics of relations, functions, the Peano Axioms, Axiom of Choice, Zorn's Lemma, well ordering, countable sets, ordinal and cardinal numbers, and cardinal arithmetic. The emphasis is more on concepts than on an axiomatic development." The prerequisite is Mathematical Reasoning (MATH 3000), which also covers some of the topics of this class. A senior/graduate level class that elaborates on the ideas introduced here (and puts more of an emphasis on an axiomatic development) is Introduction to Set Theory. A more advanced class is the graduate level Set Theory class (my online notes for this material are still at the planning stage, as of spring 2023).

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). A copy of the (public domain) book is on Piazza.com.

Preface. Preface notes
Section 1. The Axiom of Extension. Section 1 notes
Section 2. The Axiom of Specification. Section 2 notes
Section 3. Unordered Pairs. Section 3 notes
Section 4. Unions and Intersections. Section 4 notes

Supplement. Proofs of Theorems in Section 4. Beamer file of Section 4 proofs of theorems
Supplement. Printout of the Proofs of Theorems in Section 4. Print file of Section 4 proofs of theorems

Section 5. Complements and Powers.
Section 6. Ordered Pairs.
Section 7. Relations.
Section 8. Functions.
Section 9. Families.
Section 10. Inverses and Composites.
Section 11. Numbers.
Section 12. The Peano Axioms.
Section 13. Arithmetic.
Section 14. Order.
Section 15. The Axiom of Choice.
Section 16. Zorn's Lemma.
Section 17. Well Ordering.
Section 18. Transfinite Recursion.
Section 19. Ordinal Numbers.
Section 20. Sets of Ordinal Numbers.
Section 21. Ordinal Arithmetic.
Section 22. The Schröder-Bernstein Theorem
Section 23. Countable Sets.
Section 24. Cardinal Arithmetic.
Section 25. Cardinal Numbers.

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