Vertical alignment using cases

Question

Using the following code, one gets the $X$ vertically aligned with the "center" of the cases. Is there a way to vertically align the $X$ with the $0$ in this output?

\documentclass{article}
\usepackage{amsmath}

\begin{document}
  \begin{equation}
    X=
    \begin{cases}
      0, & \text{if}\ a=1 \\
      1, & \text{otherwise}
    \end{cases}
  \end{equation}
\end{document}

Answer 1

You can, but the result is very dubious.*

\documentclass{article}
\usepackage{amsmath}
\usepackage{delarray}

\begin{document}

\begin{equation}
\renewcommand{\arraystretch}{1.2}
X=\begin{array}[t]\{{@{}l@{\quad}l@{}}.
  0, & \text{if $a=1$} \\
  1, & \text{otherwise}
\end{array}
\end{equation}

\begin{equation}
X=\begin{cases}
  0, & \text{if $a=1$} \\
  1, & \text{otherwise}
\end{cases}
\end{equation}

\end{document}

_{* Big understatement; actually I believe it is completely wrong. Making the brace asymmetric would be even worse. See A curly brace with an asymmetric cusp for this, I refuse to even think about it. ;-)}

Answer 2

Since cases is basically a matrix environment, a \begin{matrix} X\\ \end{matrix} should align this entry.

But it does not look nice! Don't do this!

\documentclass{article}
\usepackage{amsmath}

\begin{document}
  \begin{equation}
    \begin{matrix} X = \\
      \\
      \end{matrix}  
    \begin{cases}
      0, & \text{if}\ a=1 \\
      1, & \text{otherwise}
    \end{cases}
  \end{equation}


  \begin{equation}
    \begin{matrix} X  \\
      \\
    \end{matrix}  =
    \begin{cases}
      0, & \text{if}\ a=1 \\
      1, & \text{otherwise}
    \end{cases}
  \end{equation}


\end{document}

Answer 3

It looks nicer with a bracket. Here is a simple way to do it with the empheq package:

\documentclass{article}
\usepackage{empheq}

\begin{document}

  \begin{empheq}[left ={\begin{gathered}X=\\ ~\end{gathered}\empheqlbrack}]{gather} 
\begin{alignedat}[t]{2}
       & 0, &\quad & \text{if}\ a=1 \\
       & 1, & & \text{otherwise}
    \end{alignedat}
  \end{empheq}

\end{document}