Set Theory Symbols

{ }

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<∞}