How do I nest cases?

I am new to LaTeX. I know how to write basic equations in LaTeX. However, the following equation seems to be too difficult for me. Please help me with this. Thank you.

I'd not use the inner brace, but a standard notation for the minimum, just split across lines.

\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator{\lev}{lev}

\begin{document}

\begin{equation*}
\lev_{a,b}(i,j)=
\begin{cases}
\max(i,j) & \text{if $\min(i,j)=0$,} \1ex] \begin{aligned}[b] \min\bigl(\lev_{a,b}&(i-1,j)+1, \\ \lev_{a,b}&(i,j-1)+1, \\ \lev_{a,b}&(i-1,j-1)+1_{(a_i\ne b_j)} \bigr) \end{aligned} & \text{otherwise.} \end{cases} \end{equation*} \end{document}  You might prefer the following realization, which is obtained by using \begin{aligned} instead of \begin{aligned}[b]. amsmath's cases is defined for this. The horizontal space between the bracket and the inside contents is very good. \documentclass{article} \usepackage{amsmath} \begin{document} \[ \mathrm{lev}_{a,b}(i,j)=\begin{cases} \max(i,j)&\text{if \min(i,j)=0,}\\ \min\begin{cases} \mathrm{lev}_{a,b}(i-1,j)+1\\ \mathrm{lev}_{a,b}(i,j-1)+1\\ \mathrm{lev}_{a,b}(i-1,j-1)+1_{(a_i\ne b_j)} \end{cases} &\text{otherwise.} \end{cases}
\end{document}


It seems to me that you are writing a document which uses lev() function quite often. In this case, you should define a new macro to avoid repetition (I use \DeclareMathOperator, which is the best way for this, thanks to egreg's suggestion in his comment).

\documentclass{article}
\usepackage{amsmath}
%\newcommand{\lev}{\mathrm{lev}}: not good
\DeclareMathOperator{\lev}{lev}
\begin{document}
$\lev_{a,b}(i,j)=\begin{cases} \max(i,j)&\text{if \min(i,j)=0,}\\ \min\begin{cases} \lev_{a,b}(i-1,j)+1\\ \lev_{a,b}(i,j-1)+1\\ \lev_{a,b}(i-1,j-1)+1_{(a_i\ne b_j)} \end{cases} &\text{otherwise.} \end{cases}$
\end{document}


If you use the function lev a lot then it is a good idea to define it as follows

\newcommand{\lev}[2]{\mathrm{lev}_{a, \thinspace b} (#1, \thinspace #2)}

Just type \lev and you will get the function with two arguments to enter.

\documentclass{article}
\usepackage{amsmath}
\usepackage{booktabs}
\usepackage{array}

\begin{document}

\newcommand{\lev}[2]{\mathrm{lev}_{a, \thinspace b} (#1, \thinspace #2)}
$$\lev{i}{j} = \left\lbrace \begin{array}{l l} \max(i, \thinspace j) & \text{if~} \min(i, \thinspace j) =0, \\ \min \left\lbrace \hspace{-1mm} \begin{array}{l} \lev{i-1}{j} + 1 \\ \addlinespace[0.5mm] \lev{i}{j-1} + 1 \\ \addlinespace[0.5mm] \lev{i-1}{j-1} + 1_{(a_{i} \neq b_{j})} \end{array} \right. & \text{otherwise}. \end{array} \right.$$

\end{document}