References anf Further Reading

Textbooks

1. Sipser, Michael. "Introduction to the Theory of Computation", 3rd Edition, Cengage Learning, 2012.

   • Chapter 1: Regular Languages
   • Chapter 4: Decidability
   • Section 4.2: Uncountability

2. Rosen, Kenneth H. "Discrete Mathematics and Its Applications", 8th Edition, McGraw-Hill Education, 2019.

   • Chapter 2.5: Cardinality of Sets
   • Chapter 9.1: Relations and Their Properties
   • Chapter 9.2: n-ary Relations and Their Applications

3. Enderton, Herbert B. "Elements of Set Theory", Academic Press, 1977.

   • Chapter 6: Cardinal Numbers
   • Section 6.4: Countable Sets
   • Section 6.5: The Continuum

Online Resources

Video Lectures

1. MIT OpenCourseWare. "6.042J Mathematics for Computer Science"

   • Lecture: Infinite Sets
   • Watch Here

2. NPTEL. "Discrete Mathematics"

   • Week 2: Sets and Functions
   • Week 3: Relations
   • Access Course

Interactive Learning

1. Brilliant.org

   • Course: Infinity
   • Topic: Countable and Uncountable Sets

2. Khan Academy

   • Course: Set Theory
   • Topic: Cardinality

Tutorial Websites

1. GeeksforGeeks

   • Set Theory and Relations
   • Countable and Uncountable Sets

2. Stanford Encyclopedia of Philosophy

   • Cantor's Theorem
   • The Development of Set Theory

Research Papers

1. Cantor, Georg. "Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen" (On a Property of the Collection of All Real Algebraic Numbers), 1874.

   • Historical paper introducing the diagonalization argument
   • Available in English translation in: Ewald, William B. (ed.) "From Kant to Hilbert: A Source Book in the Foundations of Mathematics"

2. Turing, Alan M. "On Computable Numbers, with an Application to the Entscheidungsproblem", Proceedings of the London Mathematical Society, 1936.

   • Demonstrates the application of diagonalization to computability theory
   • Access via Project Euclid

Additional Learning Materials

1. Wolfram MathWorld

   • Cantor's Diagonal Method
   • Countable Set

2. Cut-the-Knot

   • Cantor's Diagonal Argument
   • Interactive demonstrations and proofs

3. American Mathematical Society

   • Feature Column: The Power of the Diagonal Argument
   • Historical context and modern applications