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:
Common Symbols Used in Set Theory
Symbols save time and space when writing. Here are the most common set symbols
In the examples C = {1, 2, 3, 4} and D = {3, 4, 5}
Symbol | Meaning | Example |
---|---|---|
{ } | Set: a collection of elements | {1, 2, 3, 4} |
A ∪ B | Union: in A or B (or both) | C ∪ D = {1, 2, 3, 4, 5} |
A ∩ B | Intersection: in both A and B | C ∩ D = {3, 4} |
A ⊆ B | Subset: every element of A is in B. | {3, 4, 5} ⊆ D |
A ⊂ B | Proper Subset: every element of A is in B, but B has more elements. |
{3, 5} ⊂ D |
A ⊄ B | Not a Subset: A is not a subset of B | {1, 6} ⊄ C |
A ⊇ B | Superset: A has same elements as B, or more | {1, 2, 3} ⊇ {1, 2, 3} |
A ⊃ B | Proper Superset: A has B's elements and more | {1, 2, 3, 4} ⊃ {1, 2, 3} |
A ⊅ B | Not a Superset: A is not a superset of B | {1, 2, 6} ⊅ {1, 9} |
A^{c} | Complement: elements not in A | D^{c} = {1, 2, 6, 7} When = {1, 2, 3, 4, 5, 6, 7} |
A − B | Difference: in A but not in B | {1, 2, 3, 4} − {3, 4} = {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) |
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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, x^{2}>x |
∃ | There Exists | ∃ x | x^{2}>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 |