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}
|	such that	so that	A = {x | x∈, x<0}
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	A is a subset of B. set A is included in set B.	{9,14,28} ⊆ {9,14,28}
A⊂B	proper subset / strict subset	A is a subset of B, but A is not equal to B.	{9,14} ⊂ {9,14,28}
A⊄B	not subset	set A is not a subset of set B	{9,66} ⊄ {9,14,28}
A⊇B	superset	A is a superset of B. set A includes set B	{9,14,28} ⊇ {9,14,28}
A⊃B	proper superset / strict superset	A is a superset of B, but B is not equal to A.	{9,14,28} ⊃ {9,14}
A⊅B	not superset	set A is not a superset of set B	{9,14,28} ⊅ {9,66}
2A	power set	all subsets of 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
Ac	complement	all the objects that do not belong to set A
A'	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, belongs to	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
|	vertical bar	such that	A={x|3<x<14}
ℵ0	aleph-null	infinite cardinality of natural numbers set
ℵ1	aleph-one	cardinality of countable ordinal numbers set
Ø	empty set	Ø = {}	A = Ø
	universal set	set of all possible values
ℕ0	natural numbers / whole numbers  set (with zero)	0 = {0,1,2,3,4,...}	0 ∈ 0
ℕ1	natural numbers / whole numbers  set (without zero)	1 = {1,2,3,4,5,...}	6 ∈ 1
ℤ	integer numbers set	= {...-3,-2,-1,0,1,2,3,...}	-6 ∈
ℚ	rational numbers set	= {x | x=a/b, a,b∈ and b≠0}	2/6 ∈
ℝ	real numbers set	= {x | -∞ < x <∞}	6.343434 ∈
ℂ	complex numbers set	= {z | z=a+bi, -∞<a<∞,      -∞<b<∞}	6+2i ∈

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