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 | 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 = {} | 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 ∈ |