SETS › TOPICS

https://en.wikipedia.org/wiki/List_of_set_theory_topics

• Set fundamentals

  • Memebership

  • Inclusion

    • Subset

      • Proper subset

    • Superset

    • Powerset

  • Fundamental sets

• Set operations

  • Union

  • Intersection

  • Difference

  • Complement

    • Absolute complement

    • Relative complement

  • Tuples

    • Cartesian product

    • Ordered pair

    • n-tuples

  • Set paradoxes

    • Cantor's paradox

    • Russell's paradox

  • Set Cardinality

    • Finite sets

      • Countable Finite Sets

      • Uncountable Finite Sets

    • Infinite sets

      • Countable Infinite Sets

      • Uncountable Infinite Sets

  • Reduction

  • Equinumerousity

  • Comparing sets

  • Set theory

    • Non-axiomatic theory

    • Axiomatic theory

  • Set theories

    • Naive set theories

    • Axiomatic set theories

      • ZFC Axioms:

        1. Axiom of Extensionality

        2. Axiom of Regularity (Axiom of Foundation)

        3. Axiom Schema of Specification

        4. Axiom of Pairing

        5. Axiom of Union

        6. Axiom Schema of Replacement

        7. Axiom of Infinity

        8. Axiom of Power Set

        9. Well-ordering theorem

      • Axiom of Empty Set

      • Axiom of Choice