Math Symbols

LaTeX provides native support for almost every mathematical symbol used in academia.

To use these symbols, you must be inside a math environment (e.g., $ ... $ for inline math or \begin{equation} ... \end{equation} for display math).

Common Operators

| Description | LaTeX Command | Rendered Output | |-------------|---------------|-----------------| | Plus or minus | \pm | $\pm$ | | Minus or plus | \mp | $\mp$ | | Multiplication (cross) | \times | $\times$ | | Multiplication (dot) | \cdot | $\cdot$ | | Division | \div | $\div$ | | Fractions | \frac{a}{b} | $\frac{a}{b}$ | | Square root | \sqrt{x} | $\sqrt{x}$ |

Relations and Inequalities

| Description | LaTeX Command | |-------------|---------------| | Equals | = | | Not equal | \neq | | Approximately equal | \approx | | Equivalent | \equiv | | Less than or equal | \leq | | Greater than or equal | \geq | | Proportional to | \propto |

Sets and Logic

LaTeX is exceptional for rendering discrete mathematics and set theory notation.

% Set Definition
A = \{ x \in \mathbb{R} \mid x > 0 \}

| Description | LaTeX Command | |-------------|---------------| | Element of | \in | | Not element of | \notin | | Subset | \subset | | Union | \cup | | Intersection | \cap | | Empty set | \emptyset | | For all | \forall | | Exists | \exists | | Logical AND | \land | | Logical OR | \lor |

Calculus and Limits

For calculus, the integral \int and summation \sum commands automatically scale based on whether they are inline or displayed. You use subscripts _ and superscripts ^ to define the limits.

% Display Math Summation
\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}
 
% Definite Integral
\int_{0}^{\infty} e^{-x} dx = 1