# Set theory symbols

**Set Theory:**

The branch of mathematics which deals with the formal properties of sets as units (without regard to the nature of their individual constituents) and the expression of other branches of mathematics in terms of sets.

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 | 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 = { } | 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 ∈ |

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