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 | 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} |
| 2A | 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 |
| Ac | 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} |
| ℵ0 | aleph-null | infinite cardinality of natural numbers set | |
| ℵ1 | aleph-one | cardinality of countable ordinal numbers set | |
| Ø | empty set | Ø = {} | A = Ø |
 |
universal set | set of all possible values | |
| ℕ0 | natural numbers / whole numbers set (with zero) |  0 = {0,1,2,3,4,...} |
0 ∈ 0 |
| ℕ1 | 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 ∈ |