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\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage{enumitem}
\title{Latex Example Live}
\author{Sebastiano Tronto}
\date{20-02-2021}
\newcommand{\reals}{\mathbb{R}}
\DeclareMathOperator{\sinus}{sinus}
\newtheorem{mythm}{My Theorem}[section]
\theoremstyle{definition}
\newtheorem{prop}[mythm]{Proposition}
\newtheorem{defi}{Definition}
\theoremstyle{remark}
\newtheorem*{warning}{Achtung}
\usepackage{xcolor}
\begin{document}
\maketitle
\section{Introduction}
{\color{pink} Hello, world!
This is a comment}
\texttt{This looks like computer code}
\section{Text}
\textbf{This sentence is in boldface}
\underline{\textit{italicized} maybe in a sentence \textbf{something}}
\underline{\textit{one inside the other}}
\emph{also italicized???}
This is an important sentence, maybe a quote or something, and this \emph{word} is very important. Let's make this sentence longer than one line.
{\Huge Large words}
%\appendix
\section{Math mode}
This is an inline formula \( \displaystyle \sum_i \frac{i}{22} \), it appears within the text
This is a displaystyle formula \[ \textstyle \sum_{\alpha=0}^{2^{10}} \frac2 \alpha{22} \] it appears on its own line
How sqrt works: \( \sqrt[\phi]{25} \)
\begin{flalign}
\label{eq}
e^x &= \left(\sum_{i=0}^\infty \frac{x^i}{i!} \right) = & \\
&= \left( 1 + x + \frac{x^2}2 \right)+ \frac{x^3}{6} + \cdots \nonumber
\end{flalign}
\[
\left\{ x \in \reals \quad \text{such that} \quad \frac{ \sinus(x)}{x^2}>0 \right\}\reals
\]
\[ \sum_i \]
The first equation we wrote is \eqref{eq}
\section{Environments}
\subsection{Lists}
\label{subsectionLists}
\begin{itemize}
\item One \textbf{item}
\item Another \(2+2=4\)
\item a third one \[\sum_{i=0}^n\]
\item A sublist:
\begin{itemize}
\item[+] First subitem
\item[+] and so on
\end{itemize}
\item Again in the main list
\end{itemize}
\begin{enumerate}[label=\Roman*]
\item One
\item Two
\item Actually three
\item Three (or not)
\end{enumerate}
\subsection*{Tables}
Let's write a table:
\vspace{1cm}
\begin{tabular}{r||l|c}
\hline
This is a table & second column & third column \\
\hline
Things & a & \( 2+2 = 4 \)\\
\hline
more things & b & c
\end{tabular}
\vspace{1cm}
\[
\left(\begin{array}{cc}
\int_0^1 e^x & \frac{2}{25} \\
0 & 0 \\
1111 & 234\alpha
\end{array}\right)
\]
\[
\begin{pmatrix}
\int_0^1 e^x & \frac{2}{25} \\
0 & 0 \\
1111 & 234\alpha
\end{pmatrix}
\]
\[
\begin{pmatrix}
1 & 2\\
3 & 4
\end{pmatrix}
\overset{L2\rightarrow L2+L3}\longrightarrow
\begin{pmatrix}
1 & 2\\
4 & 6
\end{pmatrix}
\]
\section{Last section}
In section \ref{subsectionLists} we saw how to write lists
\begin{mythm}[Gauss]
The equation \(2+x=4\) is true for \(x=2\).
\end{mythm}
\begin{prop}
A less important fact
\end{prop}
\begin{defi}
a definition
\end{defi}
\begin{mythm}
Another important fact.
\end{mythm}
\begin{warning}
It is a common mistake to think that \(2+2=5\)
\end{warning}
\[\binom45\]
\[ 2 \nmid 10 \]
\end{document}
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