Set symbols of set theory (Ø,U,{},∈,...)

Set Theory Symbols

List of set symbols of set theory and probability.

Table of set theory symbols

Symbol Symbol Name Meaning / definition Example

{ } set a collection of elements A = {3,7,9,14},
B = {9,14,28}

A ∩ B intersection objects that belong to set A and set B A ∩ B = {9,14}

A ∪ B union objects that belong to set A or set B A ∪ B = {3,7,9,14,28}

A ⊆ B subset subset has fewer elements or equal to the set {9,14,28} ⊆ {9,14,28}

A ⊂ B proper subset / strict subset subset has fewer elements than the set {9,14} ⊂ {9,14,28}

A ⊄ B not subset left set not a subset of right set {9,66} ⊄ {9,14,28}

A ⊇ B superset set A has more elements or equal to the set B {9,14,28} ⊇ {9,14,28}

A ⊃ B proper superset / strict superset set A has more elements than set B {9,14,28} ⊃ {9,14}

A ⊅ B not superset set A is not a superset of set B {9,14,28} ⊅ {9,66}

2^A power set all subsets of A

$\mathcal{P}(A)$ power set all subsets of A

A = B equality both sets have the same members A={3,9,14},
B={3,9,14},
A=B

A^c complement all the objects that do not belong to set A

A \ B relative complement objects that belong to A and not to B A = {3,9,14},
B = {1,2,3},
A-B = {9,14}

A - B relative complement objects that belong to A and not to B A = {3,9,14},
B = {1,2,3},
A-B = {9,14}

A ∆ B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}

A ⊖ B symmetric difference objects that belong to A or B but not to their intersection A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}

a∈A element of set membership A={3,9,14}, 3 ∈ A

x∉A not element of no set membership A={3,9,14}, 1 ∉ A

(a,b) ordered pair collection of 2 elements

A×B cartesian product set of all ordered pairs from A and B

|A| cardinality the number of elements of set A A={3,9,14}, |A|=3

#A cardinality the number of elements of set A A={3,9,14}, #A=3

aleph-null infinite cardinality of natural numbers set

aleph-one cardinality of countable ordinal numbers set

Ø empty set Ø = { } C = {Ø}

$\mathbb{U}$ universal set set of all possible values

$\mathbb{N}$ ₀ natural numbers / whole numbers set (with zero) $\mathbb{N}$ ₀ = {0,1,2,3,4,...} 0 ∈ $\mathbb{N}$ ₀

$\mathbb{N}$ ₁ natural numbers / whole numbers set (without zero) $\mathbb{N}$ ₁ = {1,2,3,4,5,...} 6 ∈ $\mathbb{N}$ ₁

$\mathbb{Z}$ integer numbers set $\mathbb{Z}$ = {...-3,-2,-1,0,1,2,3,...} -6 ∈ $\mathbb{Z}$

$\mathbb{Q}$ rational numbers set $\mathbb{Q}$ = {x | x=a/b, a,b∈ $\mathbb{N}$ } 2/6 ∈ $\mathbb{Q}$

$\mathbb{R}$ real numbers set $\mathbb{R}$ = {x | -∞ < x <∞} 6.343434 ∈ $\mathbb{R}$

$\mathbb{C}$ complex numbers set $\mathbb{C}$ = {z | z=a+bi, -∞<a<∞, -∞<b<∞} 6+2i ∈ $\mathbb{C}$

Statistical symbols ►

See also

Probability & statistics symbols

Basic math symbols

Logic symbols

Probability & statistics

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A = {3,7,9,14}, B = {9,14,28}
A ∩ B	intersection	objects that belong to set A and set B	A ∩ B = {9,14}
A ∪ B	union	objects that belong to set A or set B	A ∪ B = {3,7,9,14,28}
A ⊆ B	subset	subset has fewer elements or equal to the set	{9,14,28} ⊆ {9,14,28}
A ⊂ B	proper subset / strict subset	subset has fewer elements than the set	{9,14} ⊂ {9,14,28}
A ⊄ B	not subset	left set not a subset of right set	{9,66} ⊄ {9,14,28}
A ⊇ B	superset	set A has more elements or equal to the set B	{9,14,28} ⊇ {9,14,28}
A ⊃ B	proper superset / strict superset	set A has more elements than set B	{9,14,28} ⊃ {9,14}
A ⊅ B	not superset	set A is not a superset of set B	{9,14,28} ⊅ {9,66}
2^A	power set	all subsets of A
$\mathcal{P}(A)$	power set	all subsets of A
A = B	equality	both sets have the same members	A={3,9,14}, B={3,9,14}, A=B
A^c	complement	all the objects that do not belong to set A
A \ B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A-B = {9,14}
A - B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A-B = {9,14}
A ∆ B	symmetric difference	objects that belong to A or B but not to their intersection	A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14}
A ⊖ B	symmetric difference	objects that belong to A or B but not to their intersection	A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14}
a∈A	element of	set membership	A={3,9,14}, 3 ∈ A
x∉A	not element of	no set membership	A={3,9,14}, 1 ∉ A
(a,b)	ordered pair	collection of 2 elements
A×B	cartesian product	set of all ordered pairs from A and B
\|A\|	cardinality	the number of elements of set A	A={3,9,14}, \|A\|=3
#A	cardinality	the number of elements of set A	A={3,9,14}, #A=3
	aleph-null	infinite cardinality of natural numbers set
	aleph-one	cardinality of countable ordinal numbers set
Ø	empty set	Ø = { }	C = {Ø}
$\mathbb{U}$	universal set	set of all possible values
$\mathbb{N}$ ₀	natural numbers / whole numbers set (with zero)	$\mathbb{N}$ ₀ = {0,1,2,3,4,...}	0 ∈ $\mathbb{N}$ ₀
$\mathbb{N}$ ₁	natural numbers / whole numbers set (without zero)	$\mathbb{N}$ ₁ = {1,2,3,4,5,...}	6 ∈ $\mathbb{N}$ ₁
$\mathbb{Z}$	integer numbers set	$\mathbb{Z}$ = {...-3,-2,-1,0,1,2,3,...}	-6 ∈ $\mathbb{Z}$
$\mathbb{Q}$	rational numbers set	$\mathbb{Q}$ = {x \| x=a/b, a,b∈ $\mathbb{N}$ }	2/6 ∈ $\mathbb{Q}$
$\mathbb{R}$	real numbers set	$\mathbb{R}$ = {x \| -∞ < x <∞}	6.343434 ∈ $\mathbb{R}$
$\mathbb{C}$	complex numbers set	$\mathbb{C}$ = {z \| z=a+bi, -∞<a<∞, -∞<b<∞}	6+2i ∈ $\mathbb{C}$

Set Theory Symbols

Table of set theory symbols

See also

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