3

This is the first time I've ever used TeX and I'm super confused as to why this is happening. When I used the flalign* environment within the enumerate environment, it leaves line break after the item number 2., when I'd really like to have the equation begin on the same line as number 2., as it does with number 1.

\documentclass{article}
\date{}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{tikz}
\addtolength{\oddsidemargin}{-.875in}
\addtolength{\evensidemargin}{-.875in}
\addtolength{\textwidth}{1.75in}
\addtolength{\topmargin}{-.875in}
\addtolength{\textheight}{1.75in}


\begin{document}
\textbf{Question 3.6.}
\begin{enumerate}
\item $\mathcal{P}(\emptyset)=\{\emptyset\}$
\item\begin{flalign*}
\mathcal{P}\Big(\mathcal{P}\big(\mathcal{P}(\emptyset)\big)\Big)&=\mathcal{P}\Big(\mathcal{P}\big(\{\emptyset\}\big)\Big)&\\
\mathcal{P}\big(\{\emptyset\}\big)&=\big\{\emptyset ,\{\emptyset\}\big\}\\
\mathcal{P}\Big(\mathcal{P}\big(\mathcal{P}(\emptyset)\big)\Big)&=\mathcal{P}\big(\big\{\emptyset ,\{\emptyset\}\big\}\big)\\
&=\Big\{\emptyset , \{\emptyset\},\big\{\{\emptyset\}\big\}, \big\{\emptyset ,\{\emptyset\}\big\}\Big\}
\end{flalign*}
\end{enumerate}
\end{document}

enter image description here

Any help would be greatly appreciated.

2

Here is some lazy way:

\documentclass{article}
\date{}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{tikz}
\addtolength{\oddsidemargin}{-.875in}
\addtolength{\evensidemargin}{-.875in}
\addtolength{\textwidth}{1.75in}
\addtolength{\topmargin}{-.875in}
\addtolength{\textheight}{1.75in}


\begin{document}
\textbf{Question 3.6.}
\begin{enumerate}
\setlength\abovedisplayskip{0pt}           %% new
\item $\mathcal{P}(\emptyset)=\{\emptyset\}$
\item \begin{minipage}[t]{\linewidth}      %% new
\vspace{-\baselineskip}
 \begin{flalign*}
\mathcal{P}\Big(\mathcal{P}\big(\mathcal{P}(\emptyset)\big)\Big)&=\mathcal{P}\Big(\mathcal{P}\big(\{\emptyset\}\big)\Big)&\\
\mathcal{P}\big(\{\emptyset\}\big)&=\big\{\emptyset ,\{\emptyset\}\big\}\\
\mathcal{P}\Big(\mathcal{P}\big(\mathcal{P}(\emptyset)\big)\Big)&=\mathcal{P}\big(\big\{\emptyset ,\{\emptyset\}\big\}\big)\\
&=\Big\{\emptyset , \{\emptyset\},\big\{\{\emptyset\}\big\}, \big\{\emptyset ,\{\emptyset\}\big\}\Big\}
\end{flalign*}
\end{minipage}                            %% new
\end{enumerate}
\end{document}

enter image description here

2

You're using the wrong tool: what you need is aligned:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}


\begin{document}
\textbf{Question 3.6.}
\begin{enumerate}
\item $\mathcal{P}(\emptyset)=\{\emptyset\}$
\item $\!\begin{aligned}[t]
  \mathcal{P}\Bigl(\mathcal{P}\bigl(\mathcal{P}(\emptyset)\bigr)\Bigr)&=
    \mathcal{P}\Bigl(\mathcal{P}\bigl(\{\emptyset\}\bigr)\Bigr)&\\
  \mathcal{P}\bigl(\{\emptyset\}\bigr)&=
    \bigl\{\emptyset ,\{\emptyset\}\bigr\}\\
  \mathcal{P}\Bigl(\mathcal{P}\bigl(\mathcal{P}(\emptyset)\bigr)\Bigr)&=
    \mathcal{P}\bigl(\bigl\{\emptyset ,\{\emptyset\}\bigr\}\bigr)\\
  &=\Big\{\emptyset , \{\emptyset\},\bigl\{\{\emptyset\}\bigr\}, 
    \bigl\{\emptyset ,\{\emptyset\}\bigr\}\Big\}
\end{aligned}$
\end{enumerate}
\end{document}

The \! before \begin{aligned}[t] has been discussed in Why is there a \, space at the beginning of the "aligned" environment?

enter image description here

Note that \big and \Big are wrong and you should use \bigl or \Bigl for the opening fences and \bigr or \Bigr for the closing ones.

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