How to remove unnecessary space in flalign* environment

Question

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}

Any help would be greatly appreciated.

Answer 1

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}

Answer 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?

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.