set theory

Introduction
Introduction to naive set theory
- Fundamental set concepts
  - Operations on sets
  - Relations in set theory
- Essential features of Cantorian set theory
  - Equivalent sets
  - Cardinality and transfinite numbers
Axiomatic set theory
- The Zermelo-Fraenkel axioms
  - Schemas for generating well-formed formulas
  - Axioms for compounding sets
  - Axioms for infinite and ordered sets
  - Schema for transfinite induction and ordinal arithmetic
  - Axiom for eliminating infinite descending species
- The Neumann-Bernays-Gödel axioms
- Limitations of axiomatic set theory
- Present status of axiomatic set theory

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$A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”$

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A page from a first-grade workbook typical of “new math” might state: “Draw connecting...

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