## 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 | 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} |

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, 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| | 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} |

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+2i ∈ |