List of set symbols of set theory and probability.

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 | 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 | ||

P(A) |
power set | all subsets of A | |

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 |

A^{c} |
complement | all the objects that do not belong to set A | |

A' | 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×B = {(a,b)|a∈A , b∈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} |

ℵ_{0} |
aleph-null | infinite cardinality of natural numbers set | |

ℵ_{1} |
aleph-one | cardinality of countable ordinal numbers set | |

Ø | empty set | Ø = {} | A = Ø |

universal set | set of all possible values | ||

ℕ_{0} |
natural numbers / whole numbers set (with zero) | _{0} = {0,1,2,3,4,...} |
0 ∈ _{0} |

ℕ_{1} |
natural numbers / whole numbers set (without zero) | _{1} = {1,2,3,4,5,...} |
6 ∈ _{1} |

ℤ |
integer numbers set | = {...-3,-2,-1,0,1,2,3,...} | -6 ∈ |

ℚ |
rational numbers set | = {x | x=a/b,
a,b∈ and b≠0} |
2/6 ∈ |

ℝ |
real numbers set | = {x | -∞ < x <∞} |
6.343434 ∈ |

ℂ |
complex numbers set | = {z | z=a+bi, -∞<a<∞, -∞<b<∞} |
6+2i ∈ |