Header image for the post titled 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”, 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