# 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=B |

A^{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∈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 = {} | A = 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+2i ∈ |