Table of Contents

  1. The Basics
    1. Displaying Formulas
    2. Greek Letters
    3. Super- and Subscripts
  2. Logic
    1. Basic Symbols
    2. Quantifier Symbols
  3. Set Theory
    1. Empty Sets and Number Sets
    2. Set Operations
  4. Order Theory
    1. Order Operations
  5. Matrices
    1. Augmented Matrices

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.

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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)