## 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 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 power set all subsets of A A = B equality both sets have the same members A={3,9,14},

B={3,9,14},

A=BA ^{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∈Aelement of set membership A={3,9,14}, 3 ∈ A x∉Anot 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 _{0}natural numbers / whole numbers set (with zero) _{0}= {0,1,2,3,4,...}0 ∈ _{0}_{1}natural numbers / whole numbers set (without zero) _{1}= {1,2,3,4,5,...}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+2 i∈

## See also