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\mathbb{R}, 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  
\mathcal{P}(A) power set all subsets of A  
P(A) power set all subsets of A  
(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×B = {(a,b)|a∈A , b∈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}
0 aleph-null infinite cardinality of natural numbers set  
1 aleph-one cardinality of countable ordinal numbers set  
Ø empty set Ø = {} A = Ø
\mathbb{U} universal set set of all possible values  
0 natural numbers / whole numbers  set (with zero) \mathbb{N}0 = {0,1,2,3,4,...} 0 ∈ \mathbb{N}0
1 natural numbers / whole numbers  set (without zero) \mathbb{N}1 = {1,2,3,4,5,...} 6 ∈ \mathbb{N}1
integer numbers set \mathbb{Z} = {...-3,-2,-1,0,1,2,3,...} -6 ∈ \mathbb{Z}
rational numbers set \mathbb{Q} = {x | x=a/b, a,b\mathbb{Z} and b≠0} 2/6 ∈ \mathbb{Q}
real numbers set \mathbb{R} = {x | -∞ < x <∞} 6.343434 ∈ \mathbb{R}
complex numbers set \mathbb{C} = {z | z=a+bi, -∞<a<∞,      -∞<b<∞} 6+2i\mathbb{C}

 

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