Set Theory: Set Symbols - Maths [TN201401011]

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

{ } 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: A^C e.g. U = {X, Y}, A = {X} ⇒ A' = {Y}

U = {X, Y}, A = {X} ⇒ A^C = {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

e.g.	{	...	,	1	,	...	,	0.75	,	...	,	1	,	...	}
				2

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, ...}