Set Theory Symbols
Set Theory Symbols :
Set theory symbols, such as ∪ (union), ∩ (intersection), and ⊆ (subset), are fundamental mathematical notations used to represent relationships and operations within sets. These symbols play a crucial role in expressing set concepts and relationships, simplifying complex mathematical ideas into concise representations. Understanding these symbols is essential for mastering the language of set theory.
Table of Set Theory Symbols
|
Symbol |
Symbol Name |
Meaning / definition |
|
{ } |
set |
a collection of elements |
|
| |
such that |
so that |
|
A⋂B |
intersection |
objects that belong to set A and set B |
|
A⋃B |
union |
objects that belong to set A or set B |
|
A⊆B |
subset |
A is a subset of B. set A is included in set B. |
|
A⊂B |
proper subset / strict subset |
A is a subset of B, but A is not equal to B. |
|
A⊄B |
not subset |
set A is not a subset of set B |
|
A⊇B |
superset |
A is a superset of B. set A includes set B |
|
A⊃B |
proper superset / strict superset |
A is a superset of B, but B is not equal to A. |
|
A⊅B |
not superset |
set A is not a superset of set B |
|
2A |
power set |
all subsets of A |
|
P(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 |
|
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-B |
relative complement |
objects that belong to A and not to B |
|
A∆B |
symmetric difference |
objects that belong to A or B but not to their intersection |
|
A⊖B |
symmetric difference |
objects that belong to A or B but not to their intersection |
|
a∈A |
element of, belongs to |
set membership |
|
x∉A |
not element of |
no set membership |
|
(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 |
cardinality |
the number of elements of set A |
|
| |
vertical bar |
such that |
|
ℵ0 |
aleph-null |
infinite cardinality of natural numbers set |
|
ℵ1 |
aleph-one |
cardinality of countable ordinal numbers set |
|
Ø |
empty set |
Ø = {} |
|
U |
universal set |
set of all possible values |
|
ℕ0 |
natural numbers / whole numbers set (with zero) |
0 = {0,1,2,3,4,...} |
|
ℕ1 |
natural numbers / whole numbers set (without zero) |
1 = {1,2,3,4,5,...} |
|
ℤ |
integer numbers set |
{Z} = {...-3,-2,-1,0,1,2,3,...} |
|
ℚ |
rational numbers set |
{Q} = {x | x=a/b, a,b∈{Z} and b≠0} |
|
ℝ |
real numbers set |
{R} = {x | -∞ < x <∞} |
|
ℂ |
complex numbers set |
{C} = {z | z=a+bi, -∞<a<∞, -∞<b<∞} |