Unlocking the Mysteries of Math: Dive Deep into Set Theory Symbols.
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+2 i ∈ |
They provide a foundational language for understanding and expressing various mathematical concepts and relationships, serving as the backbone for many advanced areas of math.