# Set Theory: Set Symbols

Document Reference: TN201401011 - Rev: 4.2 - Last Update: 01-02-2018 12:39 GMT - Downloaded: 13-Apr-2024 01:43 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

`U`Universal 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}
`ℝ`Real NumbersThe set of real numberse.g.   {..., -3, ..., 0, ..., π, ..., 73.2, ...}
`ℚ`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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