Symbols of a set. Jow many symbols have a set.

You never gave any. I will explain what they are though.

A set is a collection of things, usually numbers. We can list each element (or "member") of a set inside curly brackets like this:

Here is a list of common symbols used in the set theory

SymbolMeaningExample

{ }Set: a collection of elements{1, 2, 3, 4}

A ∪ BUnion: in A or B (or both)C ∪ D = {1, 2, 3, 4, 5}

A ∩ BIntersection: in both A and BC ∩ D = {3, 4}

A ⊆ BSubset: every element of A is in B.{3, 4, 5} ⊆ D

A ⊂ BProper Subset: every element of A is in B,

but B has more elements.{3, 5} ⊂ D

A ⊄ BNot a Subset: A is not a subset of B{1, 6} ⊄ C

A ⊇ BSuperset: A has same elements as B, or more{1, 2, 3} ⊇ {1, 2, 3}

A ⊃ BProper Superset: A has B's elements and more{1, 2, 3, 4} ⊃ {1, 2, 3}

A ⊅ BNot a Superset: A is not a superset of B{1, 2, 6} ⊅ {1, 9}

AcComplement: elements not in ADc = {1, 2, 6, 7}

When set universal = {1, 2, 3, 4, 5, 6, 7}

A − BDifference: in A but not in B{1, 2, 3, 4} − {3, 4} = {1, 2}

a ∈ AElement of: a is in A3 ∈ {1, 2, 3, 4}

b ∉ ANot element of: b is not in A6 ∉ {1, 2, 3, 4}

ØEmpty set = {}{1, 2} ∩ {3, 4} = Ø

set universalUniversal Set: set of all possible values

(in the area of interest)  

P(A)Power Set: all subsets of AP({1, 2}) = { {}, {1}, {2}, {1, 2} }

A = BEquality: both sets have the same members{3, 4, 5} = {5, 3, 4}

A×BCartesian Product

(set of ordered pairs from A and B){1, 2} × {3, 4}

= {(1, 3), (1, 4), (2, 3), (2, 4)}

|A|Cardinality: the number of elements of set A|{3, 4}| = 2

|Such that{ n | n > 0 } = {1, 2, 3,...}

:Such that{ n : n > 0 } = {1, 2, 3,...}

∀For All∀x>1, x2>x

For all x greater than 1

x-squared is greater than x

∃There Exists∃ x | x2>x

There exists x such that

x-squared is greater than x

∴Thereforea=b ∴ b=a

Natural NumbersNatural Numbers{1, 2, 3,...} or {0, 1, 2, 3,...}

IntegersIntegers{..., −3, −2, −1, 0, 1, 2, 3, ...}

Rational NumbersRational Numbers  

Algebraic NumbersAlgebraic Numbers  

Real NumbersReal Numbers  

Imaginary NumbersImaginary Numbers3i

Complex NumbersComplex Numbers2 + 5i

its 50 miles away from the starting point