2

I am attempting to replicate this exercise:

enter image description here

Right now, I have the following (I will include an MWE for it).

enter image description here

\documentclass[11pt]{article}

\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}

\newcommand{\N}{\mathbb{N}}

\begin{document}


\begin{enumerate}
    \item[2.] Prove the following variants of the Principle of Mathematical Induction:
    \begin{enumerate}
        \item For each $n\in\N$, let $P(n)$ be a proposition and let $n_0$ be some natural number. Suppose the following two results:
        \begin{enumerate}[label={(\Alph*)}]
            \item $P(n_0)$ is true.
            \item If $P(k)$ is true, then $P(k+1)$ is also true.
        \end{enumerate}
        Then $P(n)$ is true for all natural numbers $n$ such that $n\geq n_0$.
        \item For each $n\in\N$, let $P(n)$ be a proposition. Suppose the following two results:
        \begin{enumerate}[label={(\Alph*)}]
            \item $P(1)$ is true.
            \item If $P(r)$ is true for all $r$ such that $1\leq r\leq k$, then $P(k+1)$ is true.
        \end{enumerate}
        Then $P(n)$ is true for all natural numbers $n$.
    \end{enumerate}
\end{enumerate}


\end{document}

As can plainly be seen, my replication is exact except for the (A)-(B) lists, which I cannot figure out how to center. If I enclose them in a center environment, nothing happens. If I add \centering within the enumerate environments, both items are centered individually. If I use the varwidth solution that is generally proposed (see here), I get different formatting than what I want (I'm guessing because I load the hyperref package -- see here).

Any thoughts on how my desired formatting can be achieved, would be much appreciated, thanks!

2

varwidth is not able to do its business when hyperref wants to set anchors.

You can emulate with a tabular, if your items aren't too long. However, I also added a different approach, by simply moving the items more to the right than enumerate would do.

\documentclass[11pt]{article}

\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
\usepackage{varwidth}
\usepackage{hyperref}

\newcounter{tabitem}\newcounter{tabitemplus}
\newcommand{\tabitem}{\refstepcounter{tabitem}\makebox[\labelwidth][r]{\thetabitem\ }\ignorespaces}
\renewcommand{\theHtabitem}{\thetabitemplus\arabic{tabitem}}
\newenvironment{centerenum}[1][\Alph]
 {%
  \begin{center}
  \setcounter{tabitem}{0}\stepcounter{tabitemplus}%
  \renewcommand{\thetabitem}{(#1{tabitem})}%
  \renewcommand{\arraystretch}{1.2}
  \begin{tabular}{@{}l@{}}
 }
 {\end{tabular}\end{center}}

\newcommand{\N}{\mathbb{N}}

\begin{document}

\begin{enumerate}
% tabular
\item Prove the following variants of the Principle of Mathematical Induction:
  \begin{enumerate}
  \item For each $n\in\N$, let $P(n)$ be a proposition and let $n_0$ be some 
    natural number. Suppose the following two results:
    \begin{centerenum}
    \tabitem\label{A1} $P(n_0)$ is true.
    \\
    \tabitem\label{B1} If $P(k)$ is true, then $P(k+1)$ is also true.
    \end{centerenum}
    Then $P(n)$ is true for all natural numbers $n$ such that $n\geq n_0$.
  \item For each $n\in\N$, let $P(n)$ be a proposition. Suppose the following two results:
    \begin{centerenum}
    \tabitem\label{A2} $P(0)$ is true.
    \\
    \tabitem\label{B2} If $P(r)$ is true for all $r$ such that $0\leq r\leq k$, 
      then $P(k+1)$ is true.
    \end{centerenum}
    Then $P(n)$ is true for all natural numbers $n$.
  \end{enumerate}

% wider margin
\item Prove the following variants of the Principle of Mathematical Induction:
  \begin{enumerate}
  \item For each $n\in\N$, let $P(n)$ be a proposition and let $n_0$ be some 
    natural number. Suppose the following two results:
    \begin{enumerate}[label={(\Alph*)},leftmargin=4em]
    \item $P(n_0)$ is true.
    \item If $P(k)$ is true, then $P(k+1)$ is also true.
    \end{enumerate}
    Then $P(n)$ is true for all natural numbers $n$ such that $n\geq n_0$.
  \item For each $n\in\N$, let $P(n)$ be a proposition. Suppose the following two results:
    \begin{enumerate}[label={(\Alph*)},leftmargin=4em]
    \item $P(0)$ is true.
    \item If $P(r)$ is true for all $r$ such that $0\leq r\leq k$, then $P(k+1)$ is true.
    \end{enumerate}
    Then $P(n)$ is true for all natural numbers $n$.
  \end{enumerate}
\end{enumerate}

\end{document}

enter image description here

The second instance is much more appealing, in my opinion.

1

You need to put it in a block and then center it as one unit. The easiest would be a minipage but then you need to specify the width. An alternative then is the varwidth package that defines a variable width minipage. (In my opinion it becomes hard to read and I prefer the solution without centering).

\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
\newcommand{\N}{\mathbb{N}}

\usepackage{varwidth}

\begin{document}
\begin{enumerate}
\item[2.] Prove the following variants of the Principle of Mathematical Induction:
  \begin{enumerate}
  \item For each $n\in\N$, let $P(n)$ be a proposition and let $n_0$ be some natural number. Suppose the following two results:
    \begin{center}
      \begin{varwidth}{\linewidth}
        \begin{enumerate}[label={(\Alph*)},parsep=0pt]
        \item $P(n_0)$ is true.
        \item If $P(k)$ is true, then $P(k+1)$ is also true.
        \end{enumerate}    
      \end{varwidth}  
    \end{center}
    Then $P(n)$ is true for all natural numbers $n$ such that $n\geq n_0$.
  \item For each $n\in\N$, let $P(n)$ be a proposition. Suppose the following two results:
    \begin{center}
      \begin{varwidth}{\linewidth}
        \begin{enumerate}[label={(\Alph*)},parsep=0pt]
        \item $P(1)$ is true.
        \item If $P(r)$ is true for all $r$ such that $1\leq r\leq k$, then $P(k+1)$ is true.
        \end{enumerate}
      \end{varwidth}  
    \end{center}
    Then $P(n)$ is true for all natural numbers $n$.
  \end{enumerate}
\end{enumerate}
\end{document}

enter image description here

1
  • Hi! Thanks for your response. Unfortunately, as noted in my question, I am using hyperref and thus will need a different fix. Are you aware of any? – Shady Puck Oct 22 '20 at 7:30

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