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Set Theory: Set Symbols

Document Reference: TN201401011 - Rev: 4.2 - Last Update: 01-02-2018 12:39 GMT - Downloaded: 27-May-2019 10:05 GMT

List of common set symbols as used in set notation and probability.

Set Symbol Table

SymbolSymbol NameMeaningExample
{ }SetA set of elementse.g.   {A, B, C, D, E}
=EqualsSets have the same elementse.g.   {A, B, C} = {A, B, C}
Element ofIs an element of a sete.g.   2 ∈ {2, 4, 6, 8, 10}
Not Element ofIs not an element a sete.g.   1 ∉ {2, 4, 6, 8, 10}
Null SetAn empty set: e.g.   ∅ = { }e.g.   A = ∅
#CardinalityNumber of elements of a set


Alternative notation: |{A}|
e.g.   A = {X, Y, Z}    ⇒    #A = 3
        #{X, Y, Z} = 3

      A = {X, Y, Z}    ⇒    |A| = 3
        |{X, Y, Z}| = 3

UUniversal SetSet of all possible elements
Subset ofSubset has only some elements from a sete.g.   {A, B, C} ⊂ {A, B, C, D, E}
Not Subset ofSubset has not only some elements from a sete.g.   {A, B, F} ⊄ {A, B, C, D, E}
IntersectionElements that belong to both sets onlye.g.   {A, B, C} ∩ {B, C, D} = {B, C}
UnionElements that belong to one or the other sete.g.   {A, B} ∪ {B, C} = {A, B, C}
'ComplementAll elements that are members of U but do not belong to this set

Alternative notation: AC
e.g.  U = {X, Y},  A = {X}   ⇒  A' = {Y}


      U = {X, Y},  A = {X}   ⇒  AC = {Y}
\Set Difference
aka Relative Complement
Elements that belong to the larger set and not to the smaller set

Alternative notation: {A} − {B}
e.g.   {A, B, C, D} \ {A, B} = {C, D}


      {A, B, C, D} − {A, B} = {C, D}
Real NumbersThe set of real numberse.g.   {..., -3, ..., 0, ..., π, ..., 73.2, ...}
Rational NumbersThe set of rational numbers
e.g. {..., 1 , ..., 0.75, ..., 1, ...}
2
IntegersThe set of integers{..., -3, -2, -1, 0, 1, 2, 3, ...}
⋃ {0}n/aThe set of whole numbers{0, 1, 2, 3, 4, ...}
Natural NumbersThe set of natural numbers{1, 2, 3, 4, ...}

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