$\quad$ in different lines are not the same effect?

Question

%% AMS-LaTeX Created by Wolfram Mathematica 9.0 : www.wolfram.com

\documentclass{article}
\usepackage{amsmath, amssymb, graphics, setspace}

\newcommand{\mathsym}[1]{{}}
\newcommand{\unicode}[1]{{}}

\begin{document}

\section*{ORDERED SETS }

\subsection*{1.5 Definition}

$\quad $Let \(S\) be a set. An order on \(S\) is a relation, denoted by \(<\), with the following two properties: \\
(i) If \(x\in S\) and \(y\in S\) then one and only one of the statements

\[x<y, x=y, y<x\]

is true. \\
(ii) If \(x, y, z \in S\), if \(x < y\) and \(y < z\), then \(x < z\).

$\quad $The statement $\texttt{"}$\(x < y\) may be read as \(x\) is less than \(y\) or \(x\) is smaller than \(y\) or \(x\) precedes \(y\)$\texttt{"}$.


$\quad $It is often convenient to write \(y > x\) in place of \(x < y\).

$\quad $The notation \(x < y\) indicates that \(x < y\) or \(x = y\), without specifying which of these two is to hold. In other words, \(x < y\)
is the negation of \(x > y\).



\end{document}

Answer 1

Hacks such as $\quad$ and $\texttt{"}$ are wrong. Also \\ in normal text should be the exception, rather than a usual way to end a line.

If you want indentation after a title, load the indentfirst package. Don't “hand make” enumerated lists, but use enumerate (maybe enhancing it with enumitem).

\documentclass{article}
\usepackage{amsmath, amssymb, enumitem, indentfirst}

\newcommand{\mathsym}[1]{{}}
\newcommand{\unicode}[1]{{}}

\begin{document}

\section*{ORDERED SETS}

\subsection*{1.5 Definition}

Let \(S\) be a set. An order on \(S\) is a relation, denoted by \(<\), with the 
following two properties:
\begin{enumerate}[leftmargin=*,label=(\roman*)]
\item If \(x\in S\) and \(y\in S\) then one and only one of the statements
\[
x<y,\quad x=y,\quad y<x
\]
is true.
\item If \(x, y, z \in S\), if \(x < y\) and \(y < z\), then \(x < z\).
\end{enumerate}
The statement ``\(x < y\)'' may be read as \(x\) is less than \(y\) or \(x\) is 
smaller than \(y\) or \(x\) precedes \(y\).

It is often convenient to write \(y > x\) in place of \(x < y\).

The notation \(x < y\) indicates that \(x < y\) or \(x = y\), without specifying 
which of these two is to hold. In other words, \(x < y\) is the negation of \(x > y\).

\end{document}

Answer 2

Perhaps you should try another approach to optimize the code as well as the output.

• Use »amsthm« (or »ntheorem«) to format definitions and the like.
• Use »enumitem« to create and customize lists (as already mentioned).

All this together could give you something like this.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}
\usepackage{amssymb,amsthm}
\usepackage{enumitem}

\swapnumbers
\theoremstyle{definition}
\newtheorem{definition}{Definition}[section]

\begin{document}
  \section{Ordered Sets}
    \begin{definition}
      Let \(S\) be a set. An order on \(S\) is a relation, denoted by \(<\), with the following two properties:
      \begin{enumerate}[label={(\roman*)}]
        \item If \(x\in S\) and \(y\in S\) then one and only one of the statements
          \[
            x<y,\quad x=y,\quad y<x
          \]
        is true.
        \item If \(x, y, z \in S\), if \(x < y\) and \(y < z\), then \(x < z\).

          The statement "\(x < y\) may be read as \(x\) is less than \(y\) or \(x\) is smaller than \(y\) or \(x\) precedes \(y\)".

          It is often convenient to write \(y > x\) in place of \(x < y\).

          The notation \(x < y\) indicates that \(x < y\) or \(x = y\), without specifying which of these two is to hold. In other words, \(x < y\) is the negation of \(x > y\).
      \end{enumerate}
    \end{definition}
\end{document}

Further customization is up to you.

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