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} | | 2A | 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 | | Ac | 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 ∈ |