Set Symbols

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

{2, 4, 6, 8, … }

Three dots means goes on forever (infinite)

Common Symbols Used in Set Theory

Symbols save time and space when writing. Here are the most common set symbols

In the examples C = {0,1,2,3,4} and D = {3,4,5,6}

SymbolMeaningExample
{ }Set: a collection of elements{0,1,2,3,4}
A ∪ BUnion: in A or B (or both)C ∪ D = {0,1,2,3,4,5,6}
A ∩ BIntersection: in both A and BC ∩ D = {3,4}
A ⊆ BSubset: A has some (or all) elements of B{3,4,5,6} ⊆ D
A ⊂ BProper Subset: A has some elements of B{3,6} ⊂ D
A ⊄ BNot a Subset: A is not a subset of B{0,1} ⊄ D
A ⊇ BSuperset: A has same elements as B, or more{0,1,2} ⊇ {0,1,2}
A ⊃ BProper Superset: A has B’s elements and more{0,1,2,3} ⊃ {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 Symbol of Universal Set= {1,2,3,4,5,6,7}
A − BDifference: in A but not in B{0,1,2,3} − {3,4} = {0,1,2}
a ∈ AElement of: a is in A3 ∈ {1,2,3,4}
b ∉ ANot element of: b is not in A6 ∉ {1,2,3,4}
Empty set = {}{1,2} ∩ {3,4} = Ø
 Symbol of Universal SetUniversal 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
There Exists∃ x | x2>x
Thereforea=b ∴ b=a
 Symbol of Natural Numbers SetNatural Numbers{1,2,3,…} or {0,1,2,3,…}
 Symbol of Integer SetIntegers{…, -3, -2, -1, 0, 1, 2, 3, …}
Symbol of Rational Numbers Set Rational Numbers 
 Symbol of Algebraic Numbers SetAlgebraic Numbers 
Symbol of Real Numbers SetReal Numbers 
 Symbol of Imaginary Numbers SetImaginary Numbers3i
 Symbol of Complex Numbers SetComplex Numbers2 + 5i

Learn More

Intervals

Set-Builder Notation

Function Transformations

Inverse Functions

Sets Index

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