# LaTeX Reference

### Basics

| Symbol                   | Description              | LaTeX                 |
| ------------------------ | ------------------------ | --------------------- |
| $$\cdot$$                | Multiplication dot       | `\cdot`               |
| $$\cdots$$               | Dots                     | `\cdots`              |
| $$\frac{x}{y}$$          | Fraction                 | `\frac{x}{y}`         |
| $$\ge$$                  | Greater than or equal to | `\ge`                 |
| $$\le$$                  | Less than or equal to    | `\le`                 |
| $$\ne$$                  | Not equal to             | `\ne`                 |
| $$\sum\_{i=0}^{n}$$      | Summation                | `\sum_{i=0}^{n}`      |
| $$\infty$$               | Infinity                 | `\infty`              |
| $$\lim\_{x \to \infty}$$ | Limit                    | `\lim_{x \to \infty}` |

### Propositional Logic

| Symbol       | Description         | LaTeX      |
| ------------ | ------------------- | ---------- |
| $$\implies$$ | Implication         | `\implies` |
| $$\iff$$     | Logical equivalence | `\iff`     |
| $$\equiv$$   | Congruence          | `\equiv`   |
| $$\exists$$  | Existence           | `\exists`  |
| $$\in$$      | Inclusion           | `\in`      |
| $$\land$$    | Conjunction (and)   | `\land`    |
| $$\lor$$     | Disjunction (or)    | `\lor`     |
| $$\lnot$$    | Negation (not)      | `\lnot`    |
| $$\forall$$  | For all             | `\forall`  |
| $$\oplus$$   | Exclusive or (xor)  | `\oplus`   |

### Sets

| Symbol          | Description            | LaTeX         |
| --------------- | ---------------------- | ------------- |
| $$\mathbb{C}$$  | Complex numbers        | `\mathbb{C}`  |
| $$\mathbb{R}$$  | Real numbers           | `\mathbb{R}`  |
| $$\mathbb{Q}$$  | Rational numbers       | `\mathbb{Q}`  |
| $$\mathbb{Z}$$  | Integers               | `\mathbb{Z}`  |
| $$\mathbb{N}$$  | Natural numbers        | `\mathbb{N}`  |
| $$\mathscr{P}$$ | Power set              | `\mathscr{P}` |
| $$\cup$$        | Union (set or)         | `\cup`        |
| $$\cap$$        | Intersection (set and) | `\cap`        |
| $$\emptyset$$   | Empty Set              | `\emptyset`   |
| $$\setminus$$   | Set Division           | `\setminus`   |
| $$\subseteq$$   | Subset (inclusive)     | `\subseteq`   |

### Modular Arithmetic

| Symbol         | Description           | LaTeX      |
| -------------- | --------------------- | ---------- |
| $$p \mod q$$   | Modulo                | `\mod`     |
| $$p \pmod{q}$$ | Modulo in parentheses | `\pmod{q}` |


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