Analysis.tex

\documentclass{Math_Note}

\title{\textbf{Analysis}}
\author{Buce-Ithon}
\newdateformat{mydate}{\twodigit{\THEDAY}{ }\shortmonthname[\THEMONTH], \THEYEAR}
\date{\today}

\begin{document}
% Title page
\maketitle

% Content
\newpage
\tableofcontents
\newpage

% Surface-figure
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.24]{"./Figures/preface.jpg"}
    \caption{Math tech, autumn tea~}
\end{figure}

% Chap0-Real Number System
\setcounter{section}{-1}
\newpage
\section{Real Number}
\S 1. Rational Number Field ($\mathbb{Q}$)

\begin{df}
    A number $r$ is called a \textbf{rational number}, if $r=\frac{p}{q}$, where $p, q\in\mathbb{N}$ and $b\neq 0$.

    The set of all rational numbers is denoted by $\mathbb{Q}$, and it is called the \textbf{rational number field}.
\end{df}

\begin{nt}
    $1^{\circ}$. Proof by contradiction. -- To verify if a number is irrational.
\end{nt}

\begin{prp}
    Basic properties of rational numbers:
\end{prp}

\end{document}