3

I don't know why the end of the proof is being displayed on the next line, I want it to appear at the end of (iii)

\documentclass[11pt, a4paper]{report}
% \usepackage{eurosym}% you probably don't need this (most fonts have euro)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% \usepackage{amsmath} % you load this below
%%\usepackage{amsfonts} % you load this below
\usepackage{bm}
\usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb}
\usepackage{color}
% \usepackage{lipsum} % only for demos
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}


%\setcounter{MaxMatrixCols}{10} 10 is teh default anyway
%TCIDATA{OutputFilter=Latex.dll}
%TCIDATA{Version=5.50.0.2953}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
%TCIDATA{BibliographyScheme=Manual}
%TCIDATA{LastRevised=Sunday, November 26, 2017 16:01:29}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}

% These are sort of OK, but better to use geometry package
% to set a consistent set of page dimensions
\setlength{\textheight}{22cm}\setlength{\textwidth}{16cm}
\setlength{\topmargin}{-1.5cm}
\setlength{\oddsidemargin}{-0.5cm}\setlength{\evensidemargin}{-0.5cm}
\setlength{\textheight}{24cm}\setlength{\textwidth}{16.5cm}
\setlength{\topmargin}{-1.5cm}
\setlength{\oddsidemargin}{0.5cm}\setlength{\evensidemargin}{0.5cm}


% This discards its argument, is that intended?
% \U{wibble}  is same as \U{zzzzz}
\providecommand{\U}[1]{\protect\rule{.1in}{.1in}}


\newtheorem{theorem}{Theorem}[section]
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{Theorem}[theorem]{Theorem}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{Fact}[theorem]{Fact}

% Why all these variant corollary forms?
\newtheorem{corollary}[theorem]{Corollary}
%\newtheorem{corol}[theorem]{Corollary}
%\newtheorem{Corollary}[theorem]{Corollary}

\newtheorem{criterion}[theorem]{Criterion}

% why variant definition forms?
\newtheorem{definition}[theorem]{Definition}
%\newtheorem{Definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
% as above
\newtheorem{lemma}[theorem]{Lemma}
%\newtheorem{Lemma}[theorem]{Lemma}
\newtheorem{fact}[theorem]{Fact}
\newtheorem{lma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
% as above
\newtheorem{proposition}[theorem]{Proposition}
%\newtheorem{prop}[theorem]{Proposition}
%as above
\newtheorem{Property}[theorem]{Property}
%\newtheorem{property}[theorem]{Property}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{Comment}[theorem]{Comment}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}

% it would be better to use amsthm package for the theorem definitions
% That defines a more extensive proof environment
\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\newcommand{\ve}{\varepsilon}

%Better to use \mathrm than \text so it uses the same font in all contexts
\newcommand{\cvgpr}{\xrightarrow{\text{\upshape\tiny P}}}
\newcommand{\cvgdist}{\xrightarrow{\mathrm{d}}}
\newcommand{\G}{{\mathcal{G}}}

% \mathcal{K} not {\cal K}  %\cal not defined by default since 1993
%\newcommand{\Kx}{{\cal K}}
%\newcommand{\tod}{\to^{\cal D}}
\newcommand{\ls}{\limsup_{n\to\infty}}
\newcommand{\rE}{\mathbb{E}}
\newcommand{\A}{{\mathcal{A}}}
\newcommand{\rP}{\mathbb{P}}
\newcommand{\p}{{\mathbb{P}}}
\newcommand{\Z}{{\mathbb{Z}}}

% \mathrm{Be} not {\rm BeK}  %\cal not defined by default since 1993
%\newcommand{\Be}{{\rm Be}}
\newcommand{\re}{\mathrm{e}}
\newcommand{\ep}{\varepsilon}
%\newcommand{\Bin}{{\rm Bin}}
\newcommand{\qand}{\quad\mbox{and}\quad}
\newcommand{\quso}{\quad\mbox{so}\quad}
%\newcommand{\Nn}{{\bf N}}
%\newcommand{\St}{\underline{\rm S}}
%\newcommand{\Rt}{\underline{\rm R}}
%\newcommand{\It}{\underline{\rm I}}
%\newcommand{\one}{{\bf 1}}
\newcommand{\Ups}{{\Upsilon}}
\newcommand{\iu}{{i\mkern1mu}}
\newcommand{\II}{{\mathcal{I}}}
%\newcommand{\Var}{{\rm Var}}
%\newcommand{\var}{{\rm Var}}
%\newcommand{\Cov}{{\rm cov}}
%\newcommand{\cov}{{\rm cov}}
%\newcommand{\corr}{{\rm corr}}
%\newcommand{\lhs}{{\rm lhs}}
%\newcommand{\rhs}{{\rm rhs}}
\newcommand{\ra}{\rightarrow}
\newcommand{\I}{{\mathbf 1}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\N}{{\mathbb N}}
\newcommand{\LL}{{\mathbb L}}
\newcommand{\E}{{\mathbb{E}}}
%\newcommand{\bin}{{\rm Bin}}
%\newcommand{\Pois}{{\rm Pois}}
%\newcommand{\Po}{{\rm Pois}}
%\newcommand{\Bi}{{\cal B}}
\newcommand{\ri}{\mathrm{i}}
\newcommand{\rd}{\mathrm{d}}
\newcommand{\XXi}{\Xi_{k,m}^{(n)}}
\newcommand{\xxi}{\bar{\xi}}
\newcommand{\qedhere}{{\diamond}}
\newcommand{\eqdef}{\stackrel{\mathrm{def}}{=}}
\newcommand{\eqdist}{\stackrel{\mathrm{D}}{=}}
\newcommand{\braket}[2]{{\langle{#1|#2}\rangle}}
\newcommand{\independent}{\perp}

% use amsmath package (that you have loaded) align environment, not eqnarray
%\newcommand{\bb}{\begin{eqnarray*}}
%\newcommand{\ee}{\end{eqnarray*}}
%\newcommand{\bbb}{\begin{eqnarray}}
%\newcommand{\eee}{\end{eqnarray}}
\newcommand{\F}{{\mathcal{F}}}
\newcommand{\qed}{$\diamond$}
\newcommand{\cross}{\mathbin{\tikz [x=1.4ex,y=1.4ex,line width=.075ex] \draw (0,0) -- (1,1) (0,1) -- (1,0);}}%
% \parindent 0pt % this is just low level version of following line
% \setlength{\parindent}{0pt}% 
% use parskip package (if you must) to stop indent and put vertical space betwen paragraphs
% although most documents lok better with traditional typesetting with indentation and no vertical space
\usepackage{parskip}

%\newcommand{\forceindent}{\leavevmode{\parindent=3em\indent}}%eek



%\input{tcilatex}


\begin{document}
\begin{proposition} 
If $\chi$ is the character of a representation $\rho$ of degree $n$, then
\begin{enumerate}[label=(\roman*)]
\item $\chi(1) = n$ 
\item $\chi(s^{-1}) = \chi(s)^*\quad for s \in G$ \qquad (where $*$ denotes complex conjugation)
\item $\chi(tst^{-1})=\chi(s) \quad for s,t \in G$
\end{enumerate}

\end{proposition}

\begin{proof}
\begin{enumerate}[label=(\roman*)]
\item We have $\rho(1) = 1$, and $Tr(1)=n$ since $V$ has dimension $n$. 
\item $\rho(s^\alpha)=I$ for $\alpha$ large enough. It follows that the eigenvalues $\lambda_i$ of $\rho_s$ are roots of unity. Now with $*$ complex conjugation we have:
\[
\chi(s)^* = Tr(\rho_s)^* = \sum \lambda_i^* = \sum \lambda^{-1} = Tr(\rho_s^{-1}) = Tr(\rho_{s^{-1}}) = \chi(s^{-1})
\]
\item Using the widely known formula, $Tr(ab)=Tr(ba)$ the result follows.
\end{enumerate} 
\end{proof}




\end{document} 

EDIT: using the amsthm package:

\documentclass[11pt, a4paper]{report}
% \usepackage{eurosym}% you probably don't need this (most fonts have euro)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% \usepackage{amsmath} % you load this below
%%\usepackage{amsfonts} % you load this below
\usepackage{bm}
\usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}
\usepackage{color}
% \usepackage{lipsum} % only for demos
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}
\usepackage{parskip}

%\setcounter{MaxMatrixCols}{10} 10 is teh default anyway
%TCIDATA{OutputFilter=Latex.dll}
%TCIDATA{Version=5.50.0.2953}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
%TCIDATA{BibliographyScheme=Manual}
%TCIDATA{LastRevised=Sunday, November 26, 2017 16:01:29}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}

% These are sort of OK, but better to use geometry package
% to set a consistent set of page dimensions
\setlength{\textheight}{22cm}\setlength{\textwidth}{16cm}
\setlength{\topmargin}{-1.5cm}
\setlength{\oddsidemargin}{-0.5cm}\setlength{\evensidemargin}{-0.5cm}
\setlength{\textheight}{24cm}\setlength{\textwidth}{16.5cm}
\setlength{\topmargin}{-1.5cm}
\setlength{\oddsidemargin}{-0.1cm}\setlength{\evensidemargin}{-0.1cm}


% This discards its argument, is that intended?
% \U{wibble}  is same as \U{zzzzz}
\providecommand{\U}[1]{\protect\rule{.1in}{.1in}}


\newtheorem{theorem}{Theorem}[section]
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{Theorem}[theorem]{Theorem}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{Fact}[theorem]{Fact}

% Why all these variant corollary forms?
\newtheorem{corollary}[theorem]{Corollary}
%\newtheorem{corol}[theorem]{Corollary}
%\newtheorem{Corollary}[theorem]{Corollary}

\newtheorem{criterion}[theorem]{Criterion}

% why variant definition forms?
\newtheorem{definition}[theorem]{Definition}
%\newtheorem{Definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
% as above
\newtheorem{lemma}[theorem]{Lemma}
%\newtheorem{Lemma}[theorem]{Lemma}
\newtheorem{fact}[theorem]{Fact}
\newtheorem{lma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
% as above
\newtheorem{proposition}[theorem]{Proposition}
%\newtheorem{prop}[theorem]{Proposition}
%as above
\newtheorem{Property}[theorem]{Property}
%\newtheorem{property}[theorem]{Property}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{Comment}[theorem]{Comment}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}

% it would be better to use amsthm package for the theorem definitions
% That defines a more extensive proof environment

\newcommand{\ve}{\varepsilon}

%Better to use \mathrm than \text so it uses the same font in all contexts
\newcommand{\cvgpr}{\xrightarrow{\text{\upshape\tiny P}}}
\newcommand{\cvgdist}{\xrightarrow{\mathrm{d}}}
\newcommand{\G}{{\mathcal{G}}}

% \mathcal{K} not {\cal K}  %\cal not defined by default since 1993
%\newcommand{\Kx}{{\cal K}}
%\newcommand{\tod}{\to^{\cal D}}
\newcommand{\ls}{\limsup_{n\to\infty}}
\newcommand{\rE}{\mathbb{E}}
\newcommand{\A}{{\mathcal{A}}}
\newcommand{\rP}{\mathbb{P}}
\newcommand{\p}{{\mathbb{P}}}
\newcommand{\Z}{{\mathbb{Z}}}

% \mathrm{Be} not {\rm BeK}  %\cal not defined by default since 1993
%\newcommand{\Be}{{\rm Be}}
\newcommand{\re}{\mathrm{e}}
\newcommand{\ep}{\varepsilon}
%\newcommand{\Bin}{{\rm Bin}}
\newcommand{\qand}{\quad\mbox{and}\quad}
\newcommand{\quso}{\quad\mbox{so}\quad}
%\newcommand{\Nn}{{\bf N}}
%\newcommand{\St}{\underline{\rm S}}
%\newcommand{\Rt}{\underline{\rm R}}
%\newcommand{\It}{\underline{\rm I}}
%\newcommand{\one}{{\bf 1}}
\newcommand{\Ups}{{\Upsilon}}
\newcommand{\iu}{{i\mkern1mu}}
\newcommand{\II}{{\mathcal{I}}}
%\newcommand{\Var}{{\rm Var}}
%\newcommand{\var}{{\rm Var}}
%\newcommand{\Cov}{{\rm cov}}
%\newcommand{\cov}{{\rm cov}}
%\newcommand{\corr}{{\rm corr}}
%\newcommand{\lhs}{{\rm lhs}}
%\newcommand{\rhs}{{\rm rhs}}
\newcommand{\ra}{\rightarrow}
\newcommand{\I}{{\mathbf 1}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\N}{{\mathbb N}}
\newcommand{\LL}{{\mathbb L}}
\newcommand{\E}{{\mathbb{E}}}
%\newcommand{\bin}{{\rm Bin}}
%\newcommand{\Pois}{{\rm Pois}}
%\newcommand{\Po}{{\rm Pois}}
%\newcommand{\Bi}{{\cal B}}
\newcommand{\ri}{\mathrm{i}}
\newcommand{\rd}{\mathrm{d}}
\newcommand{\XXi}{\Xi_{k,m}^{(n)}}
\newcommand{\xxi}{\bar{\xi}}

\newcommand{\eqdef}{\stackrel{\mathrm{def}}{=}}
\newcommand{\eqdist}{\stackrel{\mathrm{D}}{=}}
\newcommand{\braket}[2]{{\langle{#1|#2}\rangle}}
\newcommand{\independent}{\perp}

% use amsmath package (that you have loaded) align environment, not eqnarray
%\newcommand{\bb}{\begin{eqnarray*}}
%\newcommand{\ee}{\end{eqnarray*}}
%\newcommand{\bbb}{\begin{eqnarray}}
%\newcommand{\eee}{\end{eqnarray}}
\newcommand{\F}{{\mathcal{F}}}

\newcommand{\cross}{\mathbin{\tikz [x=1.4ex,y=1.4ex,line width=.075ex] \draw (0,0) -- (1,1) (0,1) -- (1,0);}}%
% \parindent 0pt % this is just low level version of following line
% \setlength{\parindent}{0pt}% 
% use parskip package (if you must) to stop indent and put vertical space betwen paragraphs
% although most documents lok better with traditional typesetting with indentation and no vertical space


%\newcommand{\forceindent}{\leavevmode{\parindent=3em\indent}}%eek



%\input{tcilatex}


\begin{document}
\newpage
\pagestyle{fancy}
\fancyhf{}
\fancyhead[EL]{\nouppercase\leftmark}
\fancyhead[OR]{\nouppercase\rightmark}
\fancyhead[ER,OL]{\thepage}

\maketitle
\chapter{Introduction}
%\bigskip
%\smallskip
\section{Definitions and prerequisites}
Let us recall some basic knowledge, we begin by giving some definitions. 
%\medskip
\begin{definition} 
A group is a set $G$ together with a binary operation $*$ on $G$ satisfying
the following properties:
\begin{enumerate}[label=(G\arabic*),series=group]
\item Closure: $\forall x,y \in G, x * y \in G$.
\item Associativity: $\forall x,y, z \in G, (x * y) * z = x * (y * z)$.
\item Identity: There is an element $e \in G$ such that $e * x = x * e = x$ for all $x \in G$.
\item Inverses: For any $x \in G$ there is an element $y \in G$ such that $x * y = y * x = e$.
\end{enumerate}
\end{definition}

\begin{definition}
A group $G$ is called an abelian group if the following axiom is satisfied:
\begin{enumerate}[label=(G\arabic*),resume=group]
\item Commutativity: $\forall x,y \in G, x * y = y * x$.
\end{enumerate}
\end{definition}
\end{document}

using amsthm, the spacing breaks down

  • 2
    Don't make your own proof env, use the amsthm package and its build in proof env. Also you shoulde consider using the geometry package to se the margins instead of messing with it your self manually. – daleif Dec 21 '18 at 11:22
  • @daleif I am fairly new to Latex so I don't know how to proceed. – Maths Dec 21 '18 at 11:27
  • 1
    Add amsthm as one of your loaded packages, for example along side the amsmatrh package, then remove \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} that should be it. Note that your code looks alot like your are using Scientific Workplace, we cannot help you there as we do not have access to it. – daleif Dec 21 '18 at 12:08
  • I am using latex, not scientific word – Maths Dec 21 '18 at 12:12
  • Then why are there %TCIDATA{ all over your MWE? It is only the Scientific Workplace programme that creates those. – daleif Dec 21 '18 at 12:14
2

Please remove your working example from all unnecessary clutter in order to get a MWE. To get things correct, do:

  • load amsthm package
  • remove \newcommand{\qed}{...}
  • remove \newcommand{\qedhere}{...}
  • remove \newcommand{\qed}{...}
  • remove \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}

I felt free to remove some commands not used in the document, so the overall code looks like this:

\documentclass[11pt, a4paper]{report}
\usepackage{bm}
\usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}
\usepackage{color}
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}

\usepackage{parskip}

\setlength{\textheight}{22cm}\setlength{\textwidth}{16cm}
\setlength{\topmargin}{-1.5cm}
\setlength{\oddsidemargin}{-0.5cm}\setlength{\evensidemargin}{-0.5cm}
\setlength{\textheight}{24cm}\setlength{\textwidth}{16.5cm}
\setlength{\topmargin}{-1.5cm}
\setlength{\oddsidemargin}{0.5cm}\setlength{\evensidemargin}{0.5cm}


\begin{document}
\begin{proposition} 
    If $\chi$ is the character of a representation $\rho$ of degree $n$, then
    \begin{enumerate}[label=(\roman*)]
        \item $\chi(1) = n$ 
        \item $\chi(s^{-1}) = \chi(s)^*\quad for s \in G$ \qquad (where $*$ denotes complex conjugation)
        \item $\chi(tst^{-1})=\chi(s) \quad for s,t \in G$
    \end{enumerate}
\end{proposition}

\begin{proof}
    \begin{enumerate}[label=(\roman*)]
        \item We have $\rho(1) = 1$, and $Tr(1)=n$ since $V$ has dimension $n$. 
        \item $\rho(s^\alpha)=I$ for $\alpha$ large enough. It follows that the eigenvalues $\lambda_i$ of $\rho_s$ are roots of unity. Now with $*$ complex conjugation we have:
        \[
        \chi(s)^* = Tr(\rho_s)^* = \sum \lambda_i^* = \sum \lambda^{-1} = Tr(\rho_s^{-1}) = Tr(\rho_{s^{-1}}) = \chi(s^{-1})
        \]
        \item Using the widely known formula, $Tr(ab)=Tr(ba)$ the result follows.
    \qedhere
\end{enumerate} 
\end{proof}
\end{document} 

Note how to use \qedhere for what you asked.

  • but this proposition is contained in a much larger document, and when I used the amsthm package and removed the commands in your answer, the layout/spacing was changed(in a bad way) – Maths Dec 21 '18 at 13:23
  • @A.E Please try to post a short example that shows how the document breaks when amsthm is loaded. – Bubaya Dec 21 '18 at 15:40
  • sure, I will add it in via editing the original question – Maths Dec 21 '18 at 15:42
  • I have edited it now – Maths Dec 21 '18 at 15:47

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