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Set theory symbols

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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

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}

2A

power set

all subsets of 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}

aA

element of

set membership

A={3,9,14}, 3 A

xA

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

http://www.rapidtables.com/math/symbols/set_symbols/aleph-null.gif

aleph-null

infinite cardinality of natural numbers set

 

http://www.rapidtables.com/math/symbols/set_symbols/aleph-one.gif

aleph-one

cardinality of countable ordinal numbers set

 

Ø

empty set

Ø = { }

C = {Ø}

universal set

set of all possible values

 

0

natural numbers / whole numbers set (with zero)

0 = {0,1,2,3,4,...}

0 0

1

natural numbers / whole numbers set (without zero)

1 = {1,2,3,4,5,...}

6 1

integer numbers set

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

-6

rational numbers set

= {x | x=a/b, a,b}

2/6

real numbers set

= {x | -∞ < x <∞}

6.343434

complex numbers set

= {z | z=a+bi, -∞<a<∞, -∞<b<∞}

6+2i

 

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