## Project Gimu

Software research and development

# MathJax Cheatsheet

## The Basics

The following chapter will introduce you to the most basic commands used in MathJax and probably LaTeX.

### Displaying Formulas

Formulas can be arranged in one line by enclosing them in $...$, whereas fully displayed formulas are wrapped in $$...$$. This serves as a basis for all of the upcoming MathJax examples underneath.

### Greek Letters

Greek alphabet is conventionally used in mathematics and similar fields.
The following table contains the whole Greek alphabet along with the commands.

Codes Lowercase Uppercase
\alpha A $\alpha$ $A$
\beta B $\beta$ $B$
\gamma \Gamma $\gamma$ $\Gamma$
\delta \Delta $\delta$ $\Delta$
\epsilon E $\epsilon$ $E$
\zeta Z $\zeta$ $Z$
\eta E $\eta$ $E$
\theta \Theta $\theta$ $\Theta$
\iota I $\iota$ $I$
\kappa K $\kappa$ $K$
\lambda \Lambda $\lambda$ $\Lambda$
\mu M $\mu$ $M$
\nu N $\nu$ $N$
o O $o$ $O$
\pi \PI $\pi$ $\Pi$
\rho R $\rho$ $R$
\sigma \Sigma $\sigma$ $\Sigma$
\tau T $\tau$ $T$
\upsilon \Upsilon $\upsilon$ $\Upsilon$
\phi \Phi $\phi$ $\Phi$
\chi X $\chi$ $X$
\psi \Psi $\psi$ $\Psi$
\omega \Omega $\omega$ $\Omega$

### Super- and Subscripts

Superscripts are preceded by ^, subscripts respectively by _.
An example: x_i^2 represents $x_i^2$.
The order is exchangeable: x^2_i also displays $x^2_i$.

## Logic

### Basic Symbols

Some symbols are basically identical, the other ones are just different notations (or differ in size).

Code Symbols Meaning
\lnot and \neg $\lnot$ and $\neg$ negation
\land and \wedge $\land$ and $\wedge$ conjunction
\lor and \vee $\lor$ and $\vee$ inclusive disjunction
\equiv or \Leftrightarrow $\equiv$ or $\Leftrightarrow$ if and only if
\implies and \Longrightarrow or \Rightarrow $\implies$ and $\Longrightarrow$ or $\Rightarrow$ if a then b
\Longleftarrow or \Leftarrow\$ $\Longleftarrow$ or $\Leftarrow$ if a then b (reversed)

### Quantifier Symbols

Code Symbol Meaning
\forall $\forall$ for all
\exists $\exists$ there exists
\exists! $\exists!$ there exists exactly one
\nexists $\nexists$ there does not exist

## Set Theory

### Empty Sets and Number Sets

Blackboard bold is a popular typeface style used to indicate basic number sets.
You can either use \mathbb{TEXT} or \Bbb{TEXT} to write in blackboard bold style.

Code Symbol Meaning
\emptyset and \varnothing $\emptyset$ and $\varnothing$ empty set
\Bbb N $\Bbb N$ set of natural numbers
\Bbb Z $\Bbb Z$ set of integers
\Bbb Q $\Bbb Q$ set of rational numbers
\Bbb R $\Bbb R$ set of real numbers
\Bbb C $\Bbb C$ set of complex numbers

### Set Operations

Code Symbol Meaning
\in $\in$ is member
\notin $\notin$ is not member
\subset $\subset$ is subset
\subseteq $\subseteq$ is subset or equal
\cap $\cap$ set intersection
\cup $\cup$ set union
\setminus $\setminus$ set difference

## Order Theory

### Relation Operators

Code Symbol Meaning
\nless $\nless$ not less than
\ngtr $\ngtr$ not greater than
\leq $\leq$ less than or equal to
\geq $\geq$ greather than or equal to
\nleq $\nleq$ neither less than nor equal to
\ngeq $\ngeq$ neither greater than nor equal to
\nleqslant $\nleqslant$ neither less than nor equal to
\ngeqslant $\ngeqslant$ neither greater than nor equal to

## Matrices

Elements are placed between \begin{KEYWORD}...\end{KEYWORD} and rows are separated with \\.

Keyword Brackets
matrix No Brackets
pmatrix $(\:)$
bmatrix $[\:]$
Bmatrix $\{\}$
vmatrix $\lvert \rvert$
Vmatrix $\Vert\:\Vert$

The above table covers the most important keywords.

### Augmented Matrices

\left(
\begin{array}{cccc|c}
1 & -5 & 2i & 2i & 4i \\
4 & 5 & 6 & 3i & 0
\end{array}
\right)



It is also possible to draw matrices by enclosing a formatted table with parantheses or brackets.

$\left( \begin{array}{cccc|c} 1 & -5 & 2i & 2i & 4i \\ 4 & 5 & 6 & 3i & 0 \end{array} \right)$