# Sets: Hierarchy

*
  1. Set concepts
  2. Elementary collections
  3. unstructured collections
     * set
     * bag, multiset
     * list, sequence
     * (unordered list)
  4. notion of sets
  5. fundamental set properties
     * disorder
     * uniqueness of elements
       * multiplicity of elements
  6. set (member) element vs object
  7. Set representation
     * intensional representation
     * extensional representation
  8. Set notation
     * Roster form
     * Set builder notation
* Set cardinality
  * Finite set
    * the empty set vs nonempty set
      * the empty set
      * nonempty set
    * singleton set
    * unordered pair
  * Infinite sets
    * Infinite enumerable set
    * Infinite innumerable set
  * Set equality
    * intensional equality
    * extensional equality
    * equal sets
    * equivalent sets
    * equinumerousity
  * Universal set
* Operations on sets
  * Set union
  * Set intersection
  * Set difference
  * Set complement (negation)
  * Cartesian product, cross/dot product
* Set properties and operations
  * Cardinal number
  * Unordered pair
  * Ordered pair
  * Set covering
  * Set partitioning
  * Number of proper subsets
  * Bell Numbers
  * Natural numbers in terms of sets
* Algebraic properties of sets
  * Set identities
  * Idempotency
* Set relations
  * inclusion relation
    * subset, superset
    * proper subset, proper superset
  * membership relation
  * indexed set
  * family of sets
* Basic set relations
  * Set membership
    * Set member
    * Set paradox
    * Richard's paradox
    * Russell's paradox
  * Set inclusion
    * Disjoint sets
    * pair-wise disjoint sets
    * Overlapping sets
    * subset, superset
    * proper subset, proper superset
  * Power set
  * set product, Cartesian product
  * ordered pair
* Fundamental sets
  * The set of natural numbers
  * The set of integers
  * The set of rational numbers
  * The set of real numbers
  * The set of complex numbers
* Mathematical theories
  * Set theory
    * naive set theory
    * axiomatic set theory
    * axioms of set theory
  * Relation theory
  * Order theory
  * Domain theory
  * Function theory
