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} |
| 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 less elements or equal to the set | {9,14,28} ⊆ {9,14,28} |
| A ⊂ B | proper subset / strict subset | subset has less 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 | |
| Ƥ (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 |
| א | aleph | infinite cardinality | |
| Ø | empty set | Ø = { } | C = {Ø} |
| U | universal set | set of all possible values | |
| ℕ | natural numbers set | ℕ = {1,2,3,4,...} | 6 ∈ ℕ |
| ℤ | integer numbers set | ℤ = {...-3,-2,-1,0,1,2,3,...} | -6 ∈ ℤ |
| ℚ | rational numbers set | ℚ = {x | x=a/b, a,b∈ℕ} | 2/6 ∈ ℚ |
| ℝ | real numbers set | ℝ = {x | -∞ < x <∞} | 6.343434 ∈ ℝ |
| ℂ | complex numbers set | ℂ = {z | z=a+bi, -∞<a<∞, -∞<b<∞} | 6+2i ∈ ℂ |
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