| symbol | latex code | explanation | |
|---|---|---|---|
∈ | \in | ||
∉ | \notin | ||
⊂ | \subset | ||
⊆ | \subseteq | ||
⊄ | \nsubseteq | ||
⊃ | \supset | ||
⊇ | \supseteq | ||
∪ | \cup | ||
∩ | \cap | ||
∖ | \setminus | ||
∅ | \emptyset | ||
U | U | ||
= | = | ||
≠ | \neq | ||
⊆ | \subseteq | ||
⊂ | \subset | ||
⊇ | \supseteq | ||
⊃ | \supset | ||
ℕ | \mathbb{N} | ||
ℤ | \mathbb{Z} | ||
ℚ | \mathbb{Q} | ||
ℝ | \mathbb{R} | ||
ℂ | \mathbb{C} | ||
|A| | |A| | ||
ℵ₀ | \aleph_0 | ||
ℵ₁ | \aleph_1 | ||
2^ℵ₀ | 2^{\aleph_0} | ||
{a, b, c} | \{a, b, c\} | ||
{x | P(x)} | \{x \mid P(x)\} | ||
A × B | A \times B | Cartesian product of sets A and B | |
P(A) | \mathcal{P}(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 ⊂ B | A \subset B | ||
A = B | A = B | ||
A ∪ B | A \cup B | ||
A ∩ B | A \cap B | ||
A ∖ B | A \setminus B | ||
A △ B | A \triangle B | ||
⋂ₐₑ Aᵢ | \bigcap_{i=a}^b A_i | ||
⋃ₐₑ Aᵢ | \bigcup_{i=a}^b A_i | ||
∑_{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 | ||
⋂ Aᵢ | \bigcap A_i | ||
(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) | ||
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 | ||
A ∪ B | A \cup B | ||
A ∖ B | A \setminus B | ||
B ∖ A | B \setminus A | ||
A △ B | A \triangle B | ||
∀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 |