Question: I have this code:

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{gather*}
  \max\nolimits_X \min\nolimits_{\vec{Y}} F(X, \vec{Y})) =
  \sup\nolimits_{X} (\inf\nolimits_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \min\nolimits_{\vec{Y}} (\max\nolimits_X F(X, \vec{Y})) =
  \inf\nolimits_{\vec{Y}} (\sup\nolimits_{X} F(X, \vec{Y})) = \Gamma_2
\end{gather*}
\end{document}

```

But I want to have indexing equation. If I use `\begin{equation} ...\end{equation}`, I have not any break line.

Answer: 
The starred environments of `amsmath` such as `gather*`, `align*` and `alignat*` do not use equation numbers. Just say `gather` and the equation number will appear, unless suppressed with `\nonumber`

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{gather*}
  \max\nolimits_X \min\nolimits_{\vec{Y}} F(X, \vec{Y})) =
  \sup\nolimits_{X} (\inf\nolimits_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \min\nolimits_{\vec{Y}} (\max\nolimits_X F(X, \vec{Y})) =
  \inf\nolimits_{\vec{Y}} (\sup\nolimits_{X} F(X, \vec{Y})) = \Gamma_2
\end{gather*}

\begin{gather}
  \max\nolimits_X \min\nolimits_{\vec{Y}} F(X, \vec{Y})) =
  \sup\nolimits_{X} (\inf\nolimits_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \min\nolimits_{\vec{Y}} (\max\nolimits_X F(X, \vec{Y})) =
  \inf\nolimits_{\vec{Y}} (\sup\nolimits_{X} F(X, \vec{Y})) = \Gamma_2
\end{gather}

\end{document}

```
If you want to number the two equations as a block, use `gathered` inside `equation`, or use `gather` for both equations numbered; but perhaps `align` is even better.

```
\documentclass{article}
\usepackage{amsmath}

\DeclareMathOperator{\maxn}{max}
\DeclareMathOperator{\minn}{min}
\DeclareMathOperator{\supn}{sup}
\DeclareMathOperator{\infn}{inf}

\begin{document}

One number for the whole block
\begin{equation}
\begin{gathered}
  \maxn_X (\minn_{\vec{Y}} F(X, \vec{Y})) =
  \supn_{X} (\infn_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \minn_{\vec{Y}} (\maxn_X F(X, \vec{Y})) =
  \infn_{\vec{Y}} (\supn_{X} F(X, \vec{Y})) = \Gamma_2
\end{gathered}
\end{equation}
or numbers for both equations
\begin{gather}
  \maxn_X (\minn_{\vec{Y}} F(X, \vec{Y})) =
  \supn_{X} (\infn_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \minn_{\vec{Y}} (\maxn_X F(X, \vec{Y})) =
  \infn_{\vec{Y}} (\supn_{X} F(X, \vec{Y})) = \Gamma_2
\end{gather}
Maybe you prefer alignment at the first equal sign
\begin{align}
  \maxn_X (\minn_{\vec{Y}} F(X, \vec{Y})) &=
  \supn_{X} (\infn_{\vec{Y}} F(X, \vec{Y})) = \Gamma_1, \\
  \minn_{\vec{Y}} (\maxn_X F(X, \vec{Y})) &=
  \infn_{\vec{Y}} (\supn_{X} F(X, \vec{Y})) = \Gamma_2
\end{align}
which would enhance the symmetry between the two formulas.

\end{document}

```

I defined some new operators in order to avoid all those explicit `\nolimits`.

[![enter image description here](https://i.stack.imgur.com/nwJ75.png)](https://i.stack.imgur.com/nwJ75.png)