Document Reference: TN201401011 - Rev: 4.2 - Last Update: 01-02-2018 12:39 GMT - Downloaded: 24-Sep-2023 12:48 GMT
List of common set symbols as used in set notation and probability.
Set Symbol Table
Symbol | Symbol Name | Meaning | Example | |||||||||||||||||
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{ } | Set | A set of elements | e.g. {A, B, C, D, E} | |||||||||||||||||
= | Equals | Sets have the same elements | e.g. {A, B, C} = {A, B, C} | |||||||||||||||||
∈ | Element of | Is an element of a set | e.g. 2 ∈ {2, 4, 6, 8, 10} | |||||||||||||||||
∉ | Not Element of | Is not an element a set | e.g. 1 ∉ {2, 4, 6, 8, 10} | |||||||||||||||||
∅ | Null Set | An empty set: e.g. ∅ = { } | e.g. A = ∅ | |||||||||||||||||
# | Cardinality | Number 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 Set | Set of all possible elements | ||||||||||||||||||
⊂ | Subset of | Subset has only some elements from a set | e.g. {A, B, C} ⊂ {A, B, C, D, E} | |||||||||||||||||
⊄ | Not Subset of | Subset has not only some elements from a set | e.g. {A, B, F} ⊄ {A, B, C, D, E} | |||||||||||||||||
∩ | Intersection | Elements that belong to both sets only | e.g. {A, B, C} ∩ {B, C, D} = {B, C} | |||||||||||||||||
∪ | Union | Elements that belong to one or the other set | e.g. {A, B} ∪ {B, C} = {A, B, C} | |||||||||||||||||
' | Complement | All 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 Numbers | The set of real numbers | e.g. {..., -3, ..., 0, ..., π, ..., 73.2, ...} | |||||||||||||||||
ℚ | Rational Numbers | The set of rational numbers |
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ℤ | Integers | The set of integers | {..., -3, -2, -1, 0, 1, 2, 3, ...} | |||||||||||||||||
ℕ ⋃ {0} | n/a | The set of whole numbers | {0, 1, 2, 3, 4, ...} | |||||||||||||||||
ℕ | Natural Numbers | The set of natural numbers | {1, 2, 3, 4, ...} |