Table of Contents
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 

\beta B 

\gamma \Gamma 

\delta \Delta 

\epsilon E 

\zeta Z 

\eta E 

\theta \Theta 

\iota I 

\kappa K 

\lambda \Lambda 

\mu M 

\nu N 

o O 

\pi \PI 

\rho R 

\sigma \Sigma 

\tau T 

\upsilon \Upsilon 

\phi \Phi 

\chi X 

\psi \Psi 

\omega \Omega 
Super and Subscripts
Superscripts are preceded by ^
, subscripts respectively by _
.
An example: x_i^2
represents .
The order is exchangeable: x^2_i
also displays .
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 
and  negation 
\land and \wedge 
and  conjunction 
\lor and \vee 
and  inclusive disjunction 
\equiv or \Leftrightarrow 
or  if and only if 
\implies and \Longrightarrow or \Rightarrow 
and or  if a then b 
\Longleftarrow or \Leftarrow$ 
or  if a then b (reversed) 
Quantifier Symbols
Code  Symbol  Meaning 

\forall 
for all  
\exists 
there exists  
\exists! 
there exists exactly one  
\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 
and  empty set 
\Bbb N 
set of natural numbers  
\Bbb Z 
set of integers  
\Bbb Q 
set of rational numbers  
\Bbb R 
set of real numbers  
\Bbb C 
set of complex numbers 
Set Operations
Code  Symbol  Meaning 

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

\nless 
not less than  
\ngtr 
not greater than  
\leq 
less than or equal to  
\geq 
greather than or equal to  
\nleq 
neither less than nor equal to  
\ngeq 
neither greater than nor equal to  
\nleqslant 
neither less than nor equal to  
\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 

Vmatrix 
The above table covers the most important keywords.
Augmented Matrices
\left(
\begin{array}{ccccc}
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.