# Math rendering

## Inline math

Einstein's equation $E = mc^2$ appears inline with text.

Greek letters: $\alpha$, $\beta$, $\gamma$, $\Delta$, $\Sigma$, $\Omega$.

Subscripts and superscripts: $x_i^2$, $a_{n+1}$, $e^{i\pi} + 1 = 0$.

## Fractions and roots

The quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Simple fractions: $\frac{1}{2}$, $\frac{a+b}{c}$.

## Operators

Summation: $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$.

Product: $\prod_{k=1}^{n} k = n!$.

Integral: $\int_0^\infty e^{-x} dx = 1$.

## Display math

$$\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$$
$$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$
$$\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e$$

## Blackboard bold and font commands

$\mathbb{R}$, $\mathbb{Z}$, $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{C}$.

$\mathrm{id}$, $\mathsf{Set}$, $\text{for all } x$.

## Set notation and logic

$\forall x \in \mathbb{R}, \exists y : x^2 = y$.

$A \cup B$, $A \cap B$, $A \subseteq B$, $A \times B$.

$\neg p \lor q$, $p \land q$, $p \Rightarrow q$, $p \Leftrightarrow q$.

## Matrices (display)

$$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax + by \\ cx + dy \end{pmatrix}$$

## Arrows

$f: A \to B$, $A \hookrightarrow B$, $A \twoheadrightarrow B$.
