Latex

Latex#

Sources#

You can find some additional information here:

Comparison#

\leq - \(\leq\), \geq - \(\geq\), \approx - \(\approx\), \neq - \(\neq\), \sim - \(\sim\).

Proofs symbols#

\forall - \(\forall\), \Leftarrow - \(\Leftarrow\), \Rightarrow - \(\Rightarrow\), \Leftrightarrow - \(\Leftrightarrow\), \boxtimes - \(\boxtimes\).

Greek alphabet#

Here is a list of the Greek alphabet and the corresponding LaTeX for each letter:

Name

LaTeX

Rendered

LaTeX

Rendered

Alpha

\alpha

\(\alpha\)

A

\(A\)

Beta

\beta

\(\beta\)

B

\(B\)

Gamma

\gamma

\(\gamma\)

\Gamma

\(\Gamma\)

Delta

\delta

\(\delta\)

\Delta

\(\Delta\)

Epsilon

\epsilon

\(\epsilon\)

E

\(E\)

Zeta

\zeta

\(\zeta\)

Z

\(Z\)

Eta

\eta

\(\eta\)

H

\(H\)

Theta

\theta

\(\theta\)

\Theta

\(\Theta\)

Iota

\iota

\(\iota\)

I

\(I\)

Kappa

\kappa

\(\kappa\)

K

\(K\)

Lambda

\lambda

\(\lambda\)

\Lambda

\(\Lambda\)

Mu

\mu

\(\mu\)

M

\(M\)

Nu

\nu

\(\nu\)

N

\(N\)

Xi

\xi

\(\xi\)

\Xi

\(\Xi\)

Omicron

o

\(o\)

O

\(O\)

Pi

\pi

\(\pi\)

\Pi

\(\Pi\)

Rho

\rho

\(\rho\)

P

\(P\)

Sigma

\sigma

\(\sigma\)

\Sigma

\(\Sigma\)

Tau

\tau

\(\tau\)

T

\(T\)

Upsilon

\upsilon

\(\upsilon\)

\Upsilon

\(\Upsilon\)

Phi

\phi

\(\phi\)

\Phi

\(\Phi\)

Chi

\chi

\(\chi\)

X

\(X\)

Psi

\psi

\(\psi\)

\Psi

\(\Psi\)

Omega

\omega

\(\omega\)

\Omega

\(\Omega\)

Note: Some rendering engines interpret special commands for symbols that are identical to modern English letters — e.g., \Alpha for the symbol $A$. However, some interpreters (including browsers) do not recognize these commands, so it is recommended to use regular characters instead.

There are some special forms for classical letters:

\varphi: \(\varphi\);\varepsilon: \(\epsilon\).

Upper excreta#

  • \tilde{ffff} - \(\tilde{ffff}\), \widetilde{ffff} - \(\widetilde{ffff}\);

  • \hat{ffff} - \(\hat{ffff}\), \widehat{ffff} - \(\widehat{ffff}\);

  • \bar{ffff} - \(\bar{ffff}\), \overline{ffff} - \(\overline{ffff}\).

Operations with sets#

  • A \in B - \(A \in B\).

  • A \subset B - \(A \subset B\).

  • A \supset B - \(A \supset B\).

  • A \subseteq B - \(A \subseteq B\).

  • A \supseteq B - \(A \supseteq B\).

  • A \cup B - \(A \cup B\).

  • A \cap B - \(A \cap B\).

It is common in notation to use an operator that appears as a crossed-out version of another. In some cases, there are special symbols, such as \notin. However, in general, you can simply use the \not command before the symbol you want to negate.

  • A \notin B \not\in C - \(A \notin B \not\in C\).

  • A \not\subset B - \(A \not\subset B\).

  • A \not\supset B - \(A \not\supset B\).

  • A \not\subseteq B - \(A \not\subseteq B\).

  • A \not\supseteq B - \(A \not\supseteq B\).

  • A \notcup \not\cup B - \(A \not\cup B\).

  • A \not\cap B - \(A \not\cap B\).

Note that the symbols cup and cap sumbols look strange when combined with the not operation. It appears that they are not supposed to be used together.

Binary operators#

  • A \times B - \(A \times B\);

  • A \pm B - \(A \pm B\).

Existance#

  • \exists a - \(\exists a\);

  • \nexists a - \(\nexists a\).

Ellipses#

Ellipses is a symbol that looks like three dots in a row. They are typically used to show that some elements are omitted from the notation. These hidden elements follow a pattern that should be obvious from the explicitly stated ones.

The following tables shows typical ellipsis symbols:

Command

Rendered

Description

Example

\ldots

\(\ldots\)

Low dots are used to skip some elements of the sequnce

\(a_1, a_2, \ldots, a_n \)

\cdots

\(\cdots\)

Centered dots

\(\begin{array}{c} a_1 & a_2 & \cdots & a_n & \end{array}\)

\vdots

\(\vdots\)

Vertical dots

\(\begin{array}{ccc} a_1 \\ \vdots \\ a_2 \end{array}\)

\ddots

\(\ddots\)

Diagonal patterns

\dotsc

\(\dotsc\)

With commas

\dotsb

\(\dotsb\)

Binary operations

\dotsm

\(\dotsm\)

Multiplication

\dotsi

\(\dotsi\)

Integrals, sums

\dotso

\(\dotso\)

Miscellaneous

Vertical bar#

There is a lot of cases when vertical bars in mathematical notation can be used. And there is a set of options how you can peform that:

  • Defining conditions for sets \(\{x \in \mathbb{R} \mid x>0 \}\).

  • Conditional probability \(P(A \mid B)\).

  • It can be used as brackets for an expression; a typical expression for the Euclidean norm is \(\| A \|\).

There are few ways to create such symbol:

  • Just use | symbol: $A|B$-\(A|B\).

  • Use \mid keyword, the most typical option, create some extra spacing for symbols before and after: $A|B \mid C$- \(A|B \mid C\)

  • Use \vert keyword, I haven’t found difference with using | symbol yet: $A|B \vert C$ - \(A|B \vert C\).

  • For creating brackets as two close positioned vertical lines use \|: $\|A\|$ - \(\|A\|\).

Joining case#

The following instructions are used to create a parenthesis in latex:

  • \begin{cases} <expression>  \\end{cases} - will put expression under the bracket;

  • \\ - to jump to a new line for an expression under a bracket.

For example expression:

$$\begin{cases}
      line1; \\
      line2.
\end{cases}$$

Will show markdown:

\[\begin{split}\begin{cases} line1; \\ line2. \end{cases}\end{split}\]

Expression numbers#

Using command \tag

For example:

$$\frac{\delta}{\gamma} \tag{hello}$$
\[\frac{\delta}{\gamma} \tag{hello}\]

Brakets#

Rounding#

  • Floor \lfloor a \rfloor - \(\lfloor a \rfloor\);

  • Ceil \lceil a \rceil - \(\lceil a \rceil\);

  • Note \(\lfloor 5.31 \rfloor = 5, \lfloor -5.31 \rfloor = -6, \lceil 5.31 \rceil = 6, \lceil -5.31 \rceil=-5\).

To wrap in brackets#

Expression like:

$$[\frac{\sum_i^n}{\prod_i^n}]$$

Will be interpreted like:

\[[\frac{\sum_i^n}{\prod_i^n}]\]

The problem is that a square bracket does not completely close the expression it surrounds. To fix this, you need to put the tag $\left$ before the opening bracket and $\right$ before the closing bracket. That is, the expression:

$$\left[\frac{\sum_i^n}{\prod_i^n}\right]$$

Which will be interpreted like this:

\[\left[\frac{\sum_i^n}{\prod_i^n}\right]\]

You can even use it with types of parentheses defined by other keywords. For example expression:

\left\lceil \frac{a}{b} \right\rceil

will look like:

\[\left\lceil \frac{a}{b} \right\rceil\]

Matrices#

To create the matrix, you will need:

  • Opening and closing brackets \left(, \right);

  • The \betting{array} \end{array} instruction will allow you to create table elements inside the bracket. (in order to start the wod after opening \begin{array}, you will have to put \\);

  • The & symbol is used to move to the next element of the string;

  • To move to the next line element, the \\ is used;

  • To fill in the intermediate places between matrix elements, you may need to use multipo dots:

    • Horizontal dots \cdots - \(\cdots\);

    • Vertical dots \vdots - \(\vdots\);

    • Dianal polynomial dots - \(\ddots\):

Thus an entry of the form:

$$
\left(\begin{array}{cccc}
    a_{11} & a_{12} & \cdots & a_{1n} \\ 
    a_{21} & a_{22} & \cdots & a_{2n} \\ 
    \vdots & \vdots & \ddots & \vdots \\
    a_{n1} & a_{n2} & \cdots & a_{nn} 
\end{array}\right)
$$

Will allow you to form an expression of the form:

\[\begin{split} \left(\begin{array}{cccc} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{array}\right) \end{split}\]

Letters with empty space#

Usually used to denote moieties. To write a letter in this way, use the command \mathbb{...}.

$$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$$- \(\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}\)

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