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 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}
|
|
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
|
|
|
ℕ0
|
natural numbers / whole numbers set (with zero)
|
ℕ0 = {0,1,2,3,4,...}
|
0 ∈ ℕ0
|
|
ℕ1
|
natural numbers / whole numbers set (without
zero)
|
ℕ1 = {1,2,3,4,5,...}
|
6 ∈ ℕ1
|
|
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
|