Set Notation: Cheatsheet
My cheatsheet on mathematical set notation.
In the following examples, A = {1, 2, 3} and B = {3, 4}.
| Symbol | Meaning | Example |
|---|---|---|
| { } | Set | {1, 2, 3} |
| \( \cup \) | Union | \( A \cup B \) = {1, 2, 3, 4} |
| \( \cap \) | Intersection | \( A \cap B \) = {3} |
| \( - \) | Difference | \( A - B \) = {4} |
| \( \subset \) | Subset (proper, cannot equal to the set itself) | {1, 2} \( \subset \) A |
| \( \subseteq \) | Subset, can equal the full set | {1, 2, 3} \( \subset \) A |
| \( \in \) | Element or “in” | {1,2} \( \in \) {1, 2, 3, 4} |
| \( \supset \) | Superset | {1, 2, 3, 4}\( \supset \) {1, 2, 3} |
| \( \supseteq \) | Superset, can equal the full set | {1, 2, 3, 4}\( \supseteq \) {1, 2, 3, 4} |
| \( \emptyset \) | Empty Set | {} |
| \( \mathbb{U} \) | Universal set | Set containing all possible values. |
| \( A^\text{C}\) | Complement | Difference of a set with its universal set |
| \( \times \) | Cartesian Product | \( A \times B \) = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} |
| \( \vert A \vert \) | Cardinality (number of elements in a set) | \( \vert A \vert = 3 \) |
| | or : | “Such that” or “Given”, used in set construction | { n | n > 1 and n < 4} = {2, 3} |
| \( \forall \) | For all | \( \forall x>1, x < x^2 \) |
| \( \exists \) | There exists | \( \exists x | x = x^2 \) |
| \( \therefore \) | Therefore | \( a = b \therefore a^2 = b^2 \) |
Number sets
| Symbol | Meaning |
|---|---|
| \( \mathbb{N} \) | Natural numbers (counting numbers and 0) |
| \( \mathbb{Z} \) | Integers |
| \( \mathbb{Q} \) | Rational numbers |
| \( \mathbb{A} \) | Algebraic numbers |
| \( \mathbb{R} \) | Real numbers |
| \( \mathbb{I} \) | Imaginary numbers |
| \( \mathbb{C} \) | Complex numbers |