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 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  
\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
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}
aA element of set membership  A={3,9,14}, 3 A
xA 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{Z}} 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}

 

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See also

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