MATHGarden
  • Walk 1: About the Mathematical Garden |
  • Walk 2: The Axioms of Zermelo and Fraenkel |
  • Walk 3: The Cardinality of Sets
  • Walks
    • Walk 1: About the Mathematical Garden
      • Unit 1: What are Walks and Units?
      • Unit 2: ALSO INTERESTING
      • Unit 3: SEARCH FUNCTION in the Mathematical Garden
      • Unit 4: Existing Walks
    • Walk 2: The Axioms of Zermelo and Fraenkel
      • Unit 1: Introduction into the Axiomatics of Zermelo and Fraenkel
      • Unit 2: The Mathematical Universe
      • Unit 3: Unions and Intersections of Sets
      • Unit 4: Direct Products and Relations
      • Unit 5: Functions and Equivalent Sets
      • Unit 6: Families and the Axiom of Choice
      • Unit 7: Ordered Sets and the Lemma of Zorn
      • Unit 8: Successor Sets and the Axioms of Peano
      • Unit 9: The Natural Numbers and the Principle of Induction
    • Walk 3: The Cardinality of Sets
      • Unit 1: Finite Sets and their Cardinalities
      • Unit 2: Well-Ordered Sets
      • Unit 3: Ordinal Numbers
      • Unit 4: Cardinal Numbers
      • Unit 5: Cardinal Arithmetic
  • Mathematicians
    • Richard Dedekind
    • Georg Cantor
    • Ernst Zermelo
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Walk 3

The Cardinality of Sets

This walk deals with the foundations of mathematics. It explains how to define the cardinality of an arbitrary set (finite or infinite) and how to compute the cardinality of a set.

In particular it explains the terms $a + b$, $a \cdot b$ and $a^b$ for arbitrary cardinal numbers $a$ and $b$.

  • UNIT
    Finite Sets and their Cardinalities
  • UNIT
    Well-Ordered Sets
  • UNIT
    Ordinal Numbers
  • UNIT
    Cardinal Numbers
  • UNIT
    Cardinal Arithmetic
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