# In Latex How do you suppress the trailing "dot" after every number in the table of contents

In the contents page of a book I am writing, I get the following:
1.1. Introduction
1.1.1. Preliminary remarks
1.1.1.1. More details
and so on.
I want, for example, 1.1.1. to be just 1.1.1
I have searched the Latex Companion to no avail.
Keith
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Redefine your \section, \subsection, \subsubsection commands.
Put in preamble:
\renewcommand{\thesection}{\arabic{section}}
\renewcommand{\thesubsection}{\arabic{section}.\arabic{subsection}}
\renewcommand{\thesubsubsection}{\arabic{section}.\arabic{subsection}.\arabic{subsubsection}}
0
Author Commented:
oklit
Thanks for that; I've tried what you suggest, but it did not work.
However, your syntax seems to be an improvement on what I had.
I think the problem is embedded in amsbook.  This is the American Mathematical Society version of Latex that is, of course, ideal for maths layouts.  So I'm stuck with that.
I can control the intermediate dots, but cannot get rid of the trailing one in my contents list.  It unnecessarily takes up space and looks ugly.
Would still be grateful for other ideas.
Keith
0
Well.. it has to work :)
Please post here (or attach) your latex document (remove all unneeded (for testing purposes) content), so we can try to find out why it doesn't work for you.
0
Author Commented:
Code as requested.
Best of luck
Keith
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%\title[Short Title]{\vspace{15mm} \Huge After \,SODUKO \\ and \\ the CROSSWORD \\ \vspace{2mm}
%\huge \upshape{progress \,to} \\ \vspace{2mm}
%\Huge\itshape {serious \,MATHEMATICS}  \\ \vspace{15mm}
%\LARGE\itshape{A truely sympathetic treatment of this difficult subject \\ - written for the non-mathematician}}

\title[Short Title]{\vspace{15mm} \Huge REFRESH \,your \,interest \\ \vspace{2mm}
\huge \upshape{in \,serious} \\ \vspace{1mm}
\Huge {MATHEMATICS}  \\ \vspace{15mm}
\LARGE\itshape {A truly sympathetic treatment making access \\ \vspace{2mm} to this subject a reality for MILLIONS \\  }}

%\title[Short Title]{\vspace{15mm} \Huge Serious \,MATHEMICS \\ \vspace{2mm}
%\huge \upshape{written for} \\ \vspace{0mm}
%\Huge {Leisure \,and \,Pleasure}  \\ \vspace{15mm}
%\LARGE\itshape {A truly sympathetic treatment making access \\ \vspace{2mm} to this subject a reality for MILLIONS %\\  }}

%\title[Short Title]{\vspace{15mm} \Huge The \,\itshape {SECRETS} \\ \vspace{3mm}
%\huge \upshape{of \,understanding } \\ \vspace{3mm}
%\Huge\itshape {MATHEMATICS}  \\ \vspace{15mm}
%\LARGE\itshape{A truely sympathetic treatment of this difficult subject \\ for students, professionals and for
%leisure }}

\author[Dr A K Hannaby]{ \vspace{25mm} \LARGE Dr A K Hannaby \ PhD, \,FIMA, \,FIMechE }

%\subjclass{ \noindent \vspace{120mm} Mathematics and Engineering}

\setstretch{1.2}

\dedicatory{ \vspace{30mm} \Large Extremely \,thorough \,explanations \,of \,popular \,topics \\
in \,Mathematics \,from \,school \,to \,degree \,level \\
with \,many \,graded, \,worked \,examples \\

\setstretch{1.2}

\begin{abstract}
This is a sample document which shows the most important features
of the AMS Book or Monograph Article class.
\end{abstract}

\maketitle

%Format \chapter toc entry. Chapter
%{\MakeUppercase{\appendixname} \thecontentslabel :\hspace{1em}} % hspace ?
{\MakeUppercase{\appendixname} \thecontentslabel \hspace{-0.1em}} % hspace ?
{\vspace{2pt}}{\titlerule*[0.1pt]{}\filright\contentspage} % vspace puts space below

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\titleformat*{\section}{\normalfont\scshape} %was \titleformat*{ }

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%Format \subsection toc entry. Subsection Lss
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%Format \subsubsection toc entry.  Subsubsection Lsss
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\newpage
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\fboxrule=0.5pt
\fboxsep=2.5mm %1pt=25.4/72mm

\tableofcontents

\listoffigures

\chapter*{Preface}{\noindent
\begin{raggedright}\setstretch{0.95}
\noindent {\textit{Reasons for writing this book} \\
answered that have previously rarely even been posed. \\
\noindent\textit{Who can benefit from this book} \\
The material is presented in a way that should be understandable and enjoyable to students of both Mathematics and Mechanical Engineering, and also to many mainstream professionals who either wish to consolidate their earlier understanding, or take up the subjects as a fresh interest - perhaps on a continued professional development basis. }\\
\noindent\textit{Pre-requisite knowledge} \\
the book. \\
\noindent\textit{Arrangement of material within the book} \\
author has experienced many instances where the omission of such steps can lead to errors. \\
\end{raggedright} \vspace{3pt}
\noindent\textit{Author} \\
\noindent Dr A K Hannaby \\
\noindent $30^{\,th}$ September 2010 }

\newpage

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\setstretch{1.2}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Chapter TWO ANALYSIS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\chapter{Analysis: the idea of limit, series, continuity, convergence\,/\,divergence}
\label{sec:seriesexpansions}

\Ls{Introduction}
\label{sec:summationofseries}

\Lss{The concept of the limiting value of a function}

\noindent We write \;\; $\displaystyle{\mathop {\lim }\limits_{x\to a}\,\left\{f(x)\right\}=l}$ \;\; to mean \;\; $f(x)$ \,tends to the limit \,$l$ \;as \;$x\rightarrow a$'' \vspace{4pt}

\noindent assuming, \,of course, \,that such a limit \,$l$ \,does exist. \vspace{6pt}

\Lsss{A very simple example of a limit}
\label{sec:simplelimit}

\noindent Consider the simple case \;\; $\displaystyle{\mathop {\lim }\limits_{x\to 2}\,\left\{x^2-5\right\}}$ \vspace{6pt}

\noindent We first use an informal intuitive approach\,\ldots \; we imagine \,$x$ \,approaching the value of \,''$2$'' \,by working out \,$x^2-5$, \vspace{3pt}

\noindent first from below, \,starting with, say \,$x=1.9$ \vspace{3pt}

\hspace{35mm} $1.9^2-5$ $\rightarrow$ \; $3.61-5$ \;or \;$-1.39$ \vspace{2pt}

\hspace{39.3mm} $x=1.99$ \; $\rightarrow$ \; $-1.0399$ \vspace{2pt}

\hspace{37.6mm} $x=1.999$ \; $\rightarrow$ \; $-1.00399$ \vspace{2pt}

\hspace{36mm} $x=1.9999$ \; $\rightarrow$ \; $-1.00039999$ \vspace{4pt}

\noindent and then from above, \,starting with \,$x=2.1$ \vspace{2pt}

\hspace{37mm} $2.1^2-5$ $\rightarrow$ \; $4.41-5$ \;or \;$-0.59$ \vspace{2pt}

\hspace{39.3mm} $x=2.01$ \; $\rightarrow$ \; $-0.9599$ \vspace{2pt}

\hspace{37.6mm} $x=2.001$ \; $\rightarrow$ \; $-0.995999$ \vspace{2pt}

\hspace{36mm} $x=2.0001$ \; $\rightarrow$ \; $-0.99959999$ \vspace{6pt}

\newpage

\noindent In this example, \,the function smoothly approaches the limiting value of \,$-1$ \,as \,$x$ \,approaches the value of \,$2$, \,both from below and from above. \vspace{6pt}

\noindent On the above evidence alone, we say that \;$\displaystyle{\mathop {\lim }\limits_{x\to 2}\,\left\{x^2-5\right\}}$ \;exists \,and takes the value of \,$-1$ \vspace{3pt}

\noindent The function value at \,$x=2$ \,also happens to be \,$-1$ \vspace{6pt}

\noindent There are three separate issues involved here\,: \vspace{0pt}

\begin{enumerate}

\item \hspace{4mm} The limit of the function as \,$x$ \,approaches \,$2$ \,from below \,(from the left);

\item \hspace{4mm} The limit of the function as \,$x$ \,approaches \,$2$ \,from above \,(from the right);

\item \hspace{4mm} The value of the function precisely at \,$x=2$ \vspace{4pt}

\end{enumerate}

\noindent The reason why both \,$left$ \,and \,$right$ \,limits \,and the function value are equal, \,is because the function is \,\emph{well-behaved} \,- \,the function is continuous in the neighbourhood of \,$x=2$

\Lsss*{A less obvious example of a limit}

\noindent There are many instances where taking a limit is not so obvious; \,consider \; $\displaystyle{\mathop {\lim }\limits_{x\to 0}\,\left\{\frac{sin\,x}{x}\right\}}$ \vspace{6pt}

\noindent We have shown in our detailed treatment of trigonometric functions of small angles in para.\,\ref{sec:radianmeasureimportant}, \,that providing an angle \,$\delta\,\theta$ \,is measured in radians, \vspace{6pt}

\hspace{27mm} $\mathop {\lim }\limits_{\delta \theta\to 0} \displaystyle{\frac{{sin\,\delta \theta}}{\delta \theta}}\,=\,1$\,; \;\;\; thus \;\;\; $\mathop {\lim }\limits_{x \to 0} \displaystyle{\frac{{sin\,x}}{x}\,=\,1}$ \vspace{6pt}

\noindent the variable involved in taking the limit is, \,of course, \,of no consequence. \vspace{6pt}

\noindent It is natural to think of \,$x$ \,here as being small and $positive$ \,(so that \,$x$ \,is diminishing), and the limit is being taken \,''from the right''. \vspace{6pt}

\noindent We can emphasize this limitation by writing \;$\mathop {\lim }\limits_{\,x \to 0^{+}} \displaystyle{\frac{{sin\,x}}{x}}=1$ \vspace{6pt}

\noindent But the same is true if \,$x$ \,is small and \,$negative\ldots$ \;\; by letting \;$z=-x$ \,($z$ \,now \,$positive$), \,and reminding ourselves that\,: \; $sin(-z)=-sin\,z$ \;we can write \vspace{6pt}

\hspace{25mm} $\mathop {\lim }\limits_{\,x \to 0^{-}} \displaystyle{\frac{{sin\,x}}{x}\,=\,\mathop {\lim }\limits_{\,z \to 0^{+}} \frac{{sin(-z)}}{-z}\,=\,\mathop {\lim }\limits_{\,z \to 0^{+}} \frac{{sin\,z}}{z}=1}$ \vspace{6pt}

\noindent and so the limit applies whether we are approaching $zero$ from the $left$ or from the $right$. \vspace{3pt}

\noindent However\,, \;$\displaystyle{\frac{{sin\,x}}{x}}$ \;is not defined at \,$x=0$\,, \;being of the form \;$\displaystyle{\frac{\,0}{\,0}}$ \vspace{3pt}

\setstretch{1.45}
\noindent
\textbox{
\begin{minipage}{120mm}
\color{DarkGreen}
\noindent Notice that any quotient \;$\displaystyle{\frac{\,a}{\,b}}$ \;is taken to be such that \;$\displaystyle{\frac{\,a}{\,b}\times b=a}$ \;and if \,$b\!=\!0$\,, \,then the result will always be \,$0$ \,whatever the value of \,$a$; \,hence the value of the quotient is then indeterminate.
\end{minipage}}
\setstretch{1.2}
\vspace{6pt}

\noindent This is therefore a case where the limit of a function exists at a point, even though the function is undefined at that point. \vspace{6pt}

\Lsss*{Another important form of quotient and an example of a limit}

\vspace{3pt}\noindent Consider \;\; $\mathop {\lim }\limits_{x \to 4}\left\{\displaystyle{\frac{x^2-16}{x-4}}\right\}$  \vspace{6pt}

\noindent We can write \;\; $\displaystyle{\frac{{x^2-16}}{x-4}\,\equiv\,\frac{{(x-4)(x+4)}}{x-4}}$ \vspace{6pt}

\noindent but we cannot cancel the common factor \,$(x-4)$, \;unless we stipulate: \,$x-4\neq 0$ \vspace{6pt}

\noindent otherwise, we again would have \;$\displaystyle{\frac{\,0}{\,0}}$ \vspace{6pt}

\noindent However, \,providing \;$x\neq 4$\,, \,we can write \; $\displaystyle{\frac{{x^2-16}}{x-4}\,=\,x+4}$ \vspace{6pt}

\hspace{18mm} and hence \hspace{4mm} $\mathop {\lim }\limits_{x \to 4}\displaystyle{\frac{{x^2-16}}{x-4}\,=\,\mathop {\lim }\limits_{x \to 4}{\left\{x+4\right\}}\,=\,8}$ \vspace{9pt}

\noindent Hence this limit does exist, \,but the function is not defined at \,$x\!=\!4$

\Lss{The concept of \,$\infty$ \,(infinity)}

\noindent If \,$x$ \,becomes large and positive, \,the function \,$\displaystyle{\frac{\,1}{\,x}}$ \;becomes small and positive. \;By taking \,$x$ \,sufficiently large\,, \,$\displaystyle{\frac{\,1}{\,x}}$ \;can be made as small as we wish. \vspace{3pt}

\noindent We say that \; $\displaystyle{\frac{\,1}{\,x}}$ \,tends to \,$zero$ \;as \;$x$ \,tends to \,$\infty$\,, \;and we can write \;$\mathop {\lim }\limits_{x \to \infty}\displaystyle{\frac{\,1}{\,x}}\,=\,0$ \vspace{6pt}

\noindent It might appear that, by relating $zero$ to $\infty$ via the function $\displaystyle{\frac{1}{x}}$\,, \;this might constitute a definition of \,$\infty$. \; This is not so, \,since for example \,$\mathop {\lim }\limits_{x \to \infty}\displaystyle{\frac{\,1}{\,x^2}}\,=\,0$ \;also. \vspace{9pt}

\noindent It is perfectly permissible, \,however, \,to view of the concept of \,$\infty$ \,as: \,''that positive number which is \,$as \;large \;as \;you \;wish \;it \;to \;be$''. \; The same is true for the concept of \,$-\infty$\,; \,it is: \,''that negative number which is \,$as \;large \;as \;you \;wish \;it \;to \;be$, \,but this time, \,$negative$''.

\Ls{The formal definition of the limiting value of a function}

\noindent Formally, we say \;$f(x)\rightarrow l$ \; if, \,for any given number \,$\epsilon>0$ \,$however\,small$, \,we can find a corresponding number \,$\eta>0$ \,such that \vspace{6pt}

\hspace{22mm} $\left|f(x)-l\right|<\epsilon$ \; for all \;$x$ \;for which \; $\left|x-a\right|<\eta$ \vspace{9pt}

\noindent In this context, the value of \,$a$ \,is considered to be a constant \,(the value of \,$x$ \,where the limit is to be taken), \,and the condition: \;$\left|x-a\right|<\eta$ \;defines a neighbourhood of \,$a$. \;The smaller we take \,$\eta$ \,to be, \,the tighter will be the neighbourhood. \vspace{6pt}

\noindent This is quite a difficult concept and, \,as we will be using it later, \,it will be helpful if we look in detail at a specific example.

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Oh.. I misunderstood what you need. Now I can see that you want to remove this dot from numbers in tables of contents.

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