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: A has some (or all) elements of B | {3,4,5} ⊆ D |
A ⊂ B | Proper Subset: A has some elements of B | {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} = {3,4,5} |
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 |