Types of Sets

Read this page to become familiar with the various types of sets. This page is an aid to set terminology and notation.

  •  Cardinality of Set X:

    • n(X), Set X contains n(X) elements

  • Empty:

    • holds no elements

    • { }, Ø, n(X) = 0, |A| = 0

  • Equal:

    • two sets that contain the same elements, and no other elements

    • =, X = Y, Set X is equal to Set Y

  • Equivalent:

    • two sets not necessarily having the same elements, while having the same number of elements (the same cardinality)

    • n(X) = n(Y), Set X is equivalent to Set Y; ≈ , X ≈ Y

  • Finite:

    • holds a number of elements that is limited and countable

  • Improper Subset:

    • a set that is exactly the same as itself

  • Infinite:

    • holds a number of elements that is unlimited and uncountable

    • ∞, n(X) = ∞

  • Null:

    • also known as the empty set – the set that holds no elements

    • { }, Ø, n(X) = 0, |A| = 0

  • Proper Subset:

    • a set X that contains only elements of set Y but does not contain at least one element of Y

    • ⊂, X ⊂ Y, Set X is a proper subset of Set Y

  • Proper Superset:

    • set X holds all elements of set Y but is not equal to Y

    • ⊃, X ⊃ Y, Set X is a proper superset of Set Y

  • Power:

    • holds all subsets of a given set

    • P, X = P(Y), Set X contains all the subsets of Set Y

  • Singleton:

    • holds only one element, no more and no less

  • Subset:

    • a set X that contains only elements of set Y

    • ⊆, X ⊆ Y, Set X is a subset of Set Y

  • Superset:

    • set X contains all elements of set Y, and only elements of Y

    • ⊇, X ⊇ Y, Set X is a superset of Set Y

  • Universal:

    • holds all elements of all other sets under consideration

    • U, X = U, Set X is the universal set


Source: Saylor Academy
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Last modified: Monday, August 10, 2020, 1:20 PM