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}
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 \ 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}
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,...} \mathbb{N}6 ∈ 1
integer numbers set = {...-3,-2,-1,0,1,2,3,...} -6 ∈
rational numbers set = {x | x=a/b, a,b} 2/6 ∈
real numbers set = {x | -∞ < x <∞} 6.343434 ∈
complex numbers set = {z | z=a+bi, -∞<a<∞,      -∞<b<∞} 6+2i