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Set Theory Symbols

"Set Theory Symbols: A Brief Guide to Key Notations"| ORCHIDS

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,...}

integer numbers set

{Z} = {...-3,-2,-1,0,1,2,3,...}

rational numbers set

{Q} = {x | x=a/b, a,b∈{Z} and b≠0}

real numbers set

{R} = {x | -∞ < x <∞}

complex numbers set

{C} = {z | z=a+bi, -∞<a<∞, -∞<b<∞}

 

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