| symbol | latex code | explanation | |
|---|---|---|---|
∈ | \in | Element of a set | |
∉ | \notin | Not an element of a set | |
⊂ | \subset | Proper subset of a set | |
⊆ | \subseteq | Subset or equal to | |
⊄ | \nsubseteq | Not a subset of a set | |
⊃ | \supset | Proper superset of a set | |
⊇ | \supseteq | Superset or equal to | |
∪ | \cup | Union of sets | |
∩ | \cap | Intersection of sets | |
∖ | \setminus | Set difference | |
∅ | \emptyset | Empty set | |
U | U | Universal set | |
= | = | Equality of sets | |
≠ | \neq | Inequality of sets | |
⊆ | \subseteq | Set is a subset of another | |
⊂ | \subset | Set is a proper subset of another | |
⊇ | \supseteq | Set is a superset of another | |
⊃ | \supset | Set is a proper superset of another | |
ℕ | \mathbb{N} | Set of natural numbers | |
ℤ | \mathbb{Z} | Set of integers | |
ℚ | \mathbb{Q} | Set of rational numbers | |
ℝ | \mathbb{R} | Set of real numbers | |
ℂ | \mathbb{C} | Set of complex numbers | |
|A| | |A| | Cardinality of a set A | |
ℵ₀ | \aleph_0 | Aleph-null, the cardinality of countably infinite sets | |
ℵ₁ | \aleph_1 | Aleph-one, the next larger cardinality | |
2^ℵ₀ | 2^{\aleph_0} | Cardinality of the power set of a countably infinite set | |
{a, b, c} | \{a, b, c\} | Set containing elements a, b, and c | |
{x | P(x)} | \{x \mid P(x)\} | Set of elements x satisfying property P(x) | |
A × B | A \times B | Cartesian product of sets A and B | |
P(A) | \mathcal{P}(A) | Power set of set A | |
A ∪ ∅ = A | A \cup \emptyset = A | Union with the empty set is the set itself | |
A ∩ ∅ = ∅ | A \cap \emptyset = \emptyset | Intersection with the empty set is the empty set | |
A ∪ U = U | A \cup U = U | Union with the universal set is the universal set | |
A ∩ U = A | A \cap U = A | Intersection with the universal set is the set itself | |
A ⊆ B | A \subseteq B | A is a subset of B | |
A ⊂ B | A \subset B | A is a proper subset of B | |
A = B | A = B | A and B are equal sets | |
A ∪ B | A \cup B | Union of A and B | |
A ∩ B | A \cap B | Intersection of A and B | |
A ∖ B | A \setminus B | Difference of A and B | |
A △ B | A \triangle B | Symmetric difference of A and B | |
⋂ₐₑ Aᵢ | \bigcap_{i=a}^b A_i | Intersection of indexed family of sets | |
⋃ₐₑ Aᵢ | \bigcup_{i=a}^b A_i | Union of indexed family of sets | |
∑_{x∈A} f(x) | \sum_{x \in A} f(x) | Summation over elements of set A | |
Π_{x∈A} f(x) | \prod_{x \in A} f(x) | Product over elements of set A | |
Aᵢ | A_i | An indexed set A at index i | |
{Aᵢ | i ∈ I} | \{A_i \mid i \in I\} | Collection of sets indexed by I | |
⋃ Aᵢ | \bigcup A_i | Union of all indexed sets Aᵢ | |
⋂ Aᵢ | \bigcap A_i | Intersection of all indexed sets Aᵢ | |
(x, y) | (x, y) | Ordered pair | |
f: A → B | f: A \to B | A function f from set A to set B | |
f(x) | f(x) | Value of function f at x | |
idₐ | \text{id}_A | Identity function on set A | |
f⁻¹(B) | f^{-1}(B) | Preimage of set B under function f | |
f(A) | f(A) | Image of set A under function f | |
A ∩ B | A \cap B | Region where A and B overlap | |
A ∪ B | A \cup B | Region including A or B | |
A ∖ B | A \setminus B | Region in A but not in B | |
B ∖ A | B \setminus A | Region in B but not in A | |
A △ B | A \triangle B | Region in A or B but not both | |
∀x ∈ A, P(x) | \forall x \in A, P(x) | For all elements x in A, P(x) is true | |
∃x ∈ A, P(x) | \exists x \in A, P(x) | There exists an element x in A such that P(x) is true | |
¬∃x ∈ A, P(x) | \neg \exists x \in A, P(x) | There does not exist an x in A such that P(x) is true | |
∃!x ∈ A, P(x) | \exists! x \in A, P(x) | There exists a unique x in A such that P(x) is true |