Cardinality is a way of measuring the size of a set. Two sets have the same cardinality if they are equinumerous, i.e. if there is a bijective mapping between them. A has a larger cardinality than B if there is an injective mapping from B to A. Cardinality gives a precise way to talk about different sizes of infinity.


This concept has the prerequisites:


  • Define the relations of equinumerosity and dominance, and show that these are equivalence and order relations, respectively
  • Prove the Schroeder-Bernstein Theorem: that if two sets each dominate each other, then they are equinumerous.
  • Show that no set is equinumerous with its power set.
  • Be able to manipulate cardinal numbers algebraically
  • Be aware of the Continuum Hypothesis

Core resources (read/watch one of the following)


See also

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