# 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}

 Symbol Meaning Example { } Set: a collection of elements {0,1,2,3,4} A ∪ B Union: in A or B (or both) C ∪ D = {0,1,2,3,4,5,6} A ∩ B Intersection: in both A and B C ∩ D = {3,4} A ⊆ B Subset: A has some (or all) elements of B {3,4,5,6} ⊆ D A ⊂ B Proper Subset: A has some elements of B {3,6} ⊂ D A ⊄ B Not a Subset: A is not a subset of B {0,1} ⊄ D A ⊇ B Superset: A has same elements as B, or more {0,1,2} ⊇ {0,1,2} A ⊃ B Proper Superset: A has B’s elements and more {0,1,2,3} ⊃ {1,2,3} A ⊅ B Not a Superset: A is not a superset of B {1,2,6} ⊅ {1,9} Ac Complement: elements not in A Dc = {1,2,6,7}When  = {1,2,3,4,5,6,7} A − B Difference: in A but not in B {0,1,2,3} − {3,4} = {0,1,2} a ∈ A Element of: a is in A 3 ∈ {1,2,3,4} b ∉ A Not element of: b is not in A 6 ∉ {1,2,3,4} ∅ Empty set = {} {1,2} ∩ {3,4} = Ø  Universal Set: set of all possible values (in the area of interest) P(A) Power Set: all subsets of A P({1,2}) = { {}, {1}, {2}, {1,2} } A = B Equality: both sets have the same members {3,4,5} = {5,3,4} A×B Cartesian 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 ∴ Therefore a=b ∴ b=a  Natural Numbers {1,2,3,…} or {0,1,2,3,…}  Integers {…, -3, -2, -1, 0, 1, 2, 3, …}  Rational Numbers  Algebraic Numbers  Real Numbers  Imaginary Numbers 3i  Complex Numbers 2 + 5i