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

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

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

\newcommand{\mathsym}{{}}
\newcommand{\unicode}{{}}

\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} • Remember that you have a paragraph indentation determined by \parindent. Jul 27, 2013 at 8:47
• On looking the output and code, my observation is: in the first marked line you have \quad worked as that line immediately followed by subsection head. In other two cases you have \parindent + \quad working, which caused different indentation. Jul 27, 2013 at 11:30

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}{{}}
\newcommand{\unicode}{{}}

\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} • I use Tab in Mathematica, and then save as Tex, then Tab was converted to $quad$. I do not like all paragraphs be indented. Jul 27, 2013 at 9:14

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. 