Set symbols of set theory (Ø,U,{},∈,...)

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Set Theory Symbols

List of set symbols of set theory and probability.

Table of set theory symbols

Symbol<br>Symbol Name<br>Meaning /<br>definition<br>Example

{ }<br>set<br>a collection of elements<br>A = {3,7,9,14},<br>B = {9,14,28}

such that<br>so that<br>A = {x | x∈,

A⋂B<br>intersection<br>objects that belong to set A and set B<br>A ⋂ B = {9,14}

A⋃B<br>union<br>objects that belong to set A or set B<br>A ⋃ B = {3,7,9,14,28}

A⊆B<br>subset<br>A is a subset of B. set A is included in set B.<br>{9,14,28} ⊆ {9,14,28}

A⊂B<br>proper subset / strict subset<br>A is a subset of B, but A is not equal to B.<br>{9,14} ⊂ {9,14,28}

A⊄B<br>not subset<br>set A is not a subset of set B<br>{9,66} ⊄ {9,14,28}

A⊇B<br>superset<br>A is a superset of B. set A includes set B<br>{9,14,28} ⊇ {9,14,28}

A⊃B<br>proper superset / strict superset<br>A is a superset of B, but B is not equal to A.<br>{9,14,28} ⊃ {9,14}

A⊅B<br>not superset<br>set A is not a superset of set B<br>{9,14,28} ⊅ {9,66}

2A<br>power set<br>all subsets of A

power set<br>all subsets of A

P(A)<br>power set<br>all subsets of A

ℙ (A)<br>power set<br>all subsets of A

A=B<br>equality<br>both sets have the same members<br>A={3,9,14},<br>B={3,9,14},<br>A=B

Ac<br>complement<br>all the objects that do not belong to set A

A'<br>complement<br>all the objects that do not belong to set A

A\B<br>relative complement<br>objects that belong to A and not to B<br>A = {3,9,14},<br>B = {1,2,3},<br>A \ B = {9,14}

A-B<br>relative complement<br>objects that belong to A and not to B<br>A = {3,9,14},<br>B = {1,2,3},<br>A - B = {9,14}

A∆B<br>symmetric difference<br>objects that belong to A or B but not to their intersection<br>A = {3,9,14},<br>B = {1,2,3},<br>A ∆ B = {1,2,9,14}

A⊖B<br>symmetric difference<br>objects that belong to A or B but not to their intersection<br>A = {3,9,14},<br>B = {1,2,3},<br>A ⊖ B = {1,2,9,14}

a∈A<br>element of,<br>belongs to<br>set membership<br>A={3,9,14}, 3 ∈ A

x∉A<br>not element of<br>no set membership<br>A={3,9,14}, 1 ∉ A

(a,b)<br>ordered pair<br>collection of 2 elements

A&times;B<br>cartesian product<br>set of all ordered pairs from A and B<br>A&times;B = {(a,b)|a∈A , b∈B}

|A|<br>cardinality<br>the number of elements of set A<br>A={3,9,14}, |A|=3

#A<br>cardinality<br>the number of elements of set A<br>A={3,9,14}, #A=3

vertical bar<br>such that<br>A={x|3

&alefsym;0<br>aleph-null<br>infinite cardinality of natural numbers set

&alefsym;1<br>aleph-one<br>cardinality of countable ordinal numbers set

&Oslash;<br>empty set<br>&Oslash; = {}<br>A = &Oslash;

universal set<br>set of all possible values

ℕ 0<br>natural numbers / whole numbers set (with zero)<br>0 = {0,1,2,3,4,...}<br>0 ∈ 0

ℕ 1<br>natural numbers / whole numbers set (without zero)<br>1 = {1,2,3,4,5,...}<br>6 ∈ 1

integer numbers set<br>= {...-3,-2,-1,0,1,2,3,...}<br>-6 ∈

rational numbers set<br>= {x | x=a/b,<br>a,b∈ and b≠0}<br>2/6 ∈

real numbers set<br>= {x | -∞ x<br>6.343434 ∈

complex numbers set<br>= {z | z=a+bi, -∞ab<br>6+2i ∈

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Probability & statistics symbols

Math symbols

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