Math Symbols

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula or a mathematical expression.

Arithmetic Operators

+ (plus sign)

1. Denotes addition and is read as plus; for example, $3 + 2$.
2. Denotes that a number is positive; for example, $+2$.

− (minus sign)

1. Denotes subtraction and is read as minus; for example, $3 - 2$.
2. Denotes the additive inverse; for example, $-2$.

× (multiplication sign)

1. In elementary arithmetic, denotes multiplication; for example, $3 \times 2$.
2. In geometry and linear algebra, denotes the cross product.

÷ (division sign)

Denotes division; for example, $6 \div 2 = 3$.

= (equals sign)

Denotes equality; for example, $2 + 2 = 4$.

Comparison

< (less than)

Denotes "less than"; for example, $3 < 5$.

> (greater than)

Denotes "greater than"; for example, $5 > 3$.

≤ (less than or equal to)

Denotes "less than or equal to"; for example, $x \leq 5$.

≥ (greater than or equal to)

Denotes "greater than or equal to"; for example, $x \geq 3$.

≠ (not equal to)

Denotes "not equal to"; for example, $2 \neq 3$.

Set Theory

∈ (element of)

Denotes membership; for example, $a \in A$ means "$a$ is an element of $A$".

∉ (not an element of)

Denotes non-membership; for example, $a \notin A$.

⊂ (subset)

Denotes subset; for example, $A \subset B$ means "$A$ is a subset of $B$".

∪ (union)

Denotes set union; for example, $A \cup B$ is the union of sets $A$ and $B$.

∩ (intersection)

Denotes set intersection; for example, $A \cap B$ is the intersection of sets $A$ and $B$.

∅ (empty set)

Denotes the empty set; $\emptyset = \{ \}$.

Basic Logic

∧ (and)

Logical conjunction; for example, $P \land Q$ means "$P$ and $Q$".

∨ (or)

Logical disjunction; for example, $P \lor Q$ means "$P$ or $Q$".

¬ (not)

Logical negation; for example, $\neg P$ means "not $P$".

⇒ (implies)

Logical implication; for example, $P \Rightarrow Q$ means "if $P$ then $Q$".

⇔ (if and only if)

Logical equivalence; for example, $P \Leftrightarrow Q$ means "$P$ if and only if $Q$".

∀ (for all)

Universal quantifier; for example, $\forall x \in \mathbb{R}$ means "for all $x$ in the real numbers".

∃ (there exists)

Existential quantifier; for example, $\exists x$ means "there exists $x$".

Calculus

∫ (integral)

Denotes integration; for example, $\int f(x) \, dx$.

∂ (partial derivative)

Denotes partial derivative; for example, $\frac{\partial f}{\partial x}$.

∑ (summation)

Denotes summation; for example, $\sum_{i=1}^{n} a_i$ means the sum of $a_1$ through $a_n$.

∏ (product)

Denotes product; for example, $\prod_{i=1}^{n} a_i$ means the product of $a_1$ through $a_n$.

lim (limit)

Denotes limit; for example, $\lim_{x \to \infty} f(x)$.

Common Mathematical Constants

π (pi)

The ratio of a circle's circumference to its diameter; $\pi \approx 3.14159$.

e (Euler's number)

The base of the natural logarithm; $e \approx 2.71828$.

∞ (infinity)

Denotes infinity; for example, $\lim_{x \to \infty} f(x)$.

Number Sets

ℕ (natural numbers)

The set of natural numbers; $\mathbb{N} = \{1, 2, 3, \ldots\}$.

ℤ (integers)

The set of integers; $\mathbb{Z} = \{\ldots, -2, -1, 0, 1, 2, \ldots\}$.

ℚ (rational numbers)

The set of rational numbers; $\mathbb{Q} = \{\frac{p}{q} : p, q \in \mathbb{Z}, q \neq 0\}$.

ℝ (real numbers)

The set of real numbers.

ℂ (complex numbers)

The set of complex numbers; $\mathbb{C} = \{a + bi : a, b \in \mathbb{R}\}$.