Aligning a very long ordered pair

Question

I want display how a function assigns a very long value to an ordered pair. I am not sure where the \mapsto arrow should be placed and how much the second element in the ordered pair should be indented.

Here is a MWE.

\documentclass[paper=letter,fontsize=12pt]{scrreprt}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}

\begin{document}
\begin{equation}
        \Psi_{G}(s, t) \longmapsto \begin{aligned}
            &\big( \vee \!\{ m \in M_{G} \colon \Phi_{G}^{s}(m) - \Phi_{G}^{t}(m) > i \}, \\
            &\qquad \qquad \vee \!\{ m \in M_{G} \colon \Phi_{G}^{t}(m) - \Phi_{G}^{s}(m) > i \} \big) \text{.}
        \end{aligned}
    \end{equation}
\end{document}

Here is what the equation looks like.

Answer 1

Here's my proposal: the \mapsto should be level with the opening parenthesis.

\documentclass[paper=letter,fontsize=12pt]{scrreprt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}

\newcommand{\tbigvee}{\mathop{\mathchoice{\textstyle\bigvee}{\bigvee}{\bigvee}{\bigvee}}}

\begin{document}

\begin{equation}
\begin{aligned}
  \Psi_{G}(s, t) \mapsto {}
  &\bigl( \tbigvee \{ m \in M_{G} : \Phi_{G}^{s}(m) - \Phi_{G}^{t}(m) > i \}, \\
  &\qquad \tbigvee \{ m \in M_{G} : \Phi_{G}^{t}(m) - \Phi_{G}^{s}(m) > i \}
  \bigr).
\end{aligned}
\end{equation}

\end{document}

1. \big( and \big) are wrong, use \bigl( and \bigr)
2. \longmapsto is too long (but this is personal opinion)
3. \vee is not the right symbol to denote the supremum of a set; in this context, however, \bigvee would be too big and so I provided a reduced version
4. \colon is not the right symbol; use : to get good spacing around it

Answer 2

Is one of the following two "looks" what you're looking for? [pun intended]

\documentclass[paper=letter,fontsize=12pt]{scrreprt}
%\usepackage[utf8]{inputenc} % that's the default nowadays
%\usepackage{amsmath} % amsmath is loaded automatically mathtools
\usepackage{amssymb}
\usepackage{mathtools} % for 'pmatrix*' env.
\usepackage{relsize}
\newcommand\Vee{\mathlarger{\vee}} % 20% linear enlargement

\begin{document}
\setcounter{chapter}{1} % just for this example

\begin{equation}
\Psi_{G}(s, t) \longmapsto 
\begin{aligned}[t]
\bigl(&\Vee \{ m \in M_{G} : \Phi_{G}^{s}(m) - \Phi_{G}^{t}(m) > i \}, \\
      &\Vee \{ m \in M_{G} : \Phi_{G}^{t}(m) - \Phi_{G}^{s}(m) > i \} \bigr) 
\end{aligned}
\end{equation}

\begin{equation}
\Psi_{G}(s, t) \longmapsto 
\begin{pmatrix*}[l]
   \Vee \{ m \in M_{G} : \Phi_{G}^{s}(m) - \Phi_{G}^{t}(m) > i \}, \\
   \Vee \{ m \in M_{G} : \Phi_{G}^{t}(m) - \Phi_{G}^{s}(m) > i \} 
\end{pmatrix*}
\end{equation}

\end{document}

Answer 3

Perhaps giving each supremum a name would make this easier to read:

\documentclass[paper=letter,fontsize=12pt]{scrreprt}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}

\begin{document}

For each $s$ and $t$, define
\begin{align*}
S(s,t)&=\bigvee \bigl\{ m \in M_{G} : \Phi_{G}^{s}(m) - \Phi_{G}^{t}(m) > i \bigr\} \\
\shortintertext{and}
T(s,t)&=\bigvee \bigl\{ m \in M_{G} : \Phi_{G}^{t}(m) - \Phi_{G}^{s}(m) > i \bigr\}.
\end{align*}
Then let 
\begin{equation}
    \Psi_{G}(s, t) \longmapsto \bigl(S(s,t),T(s,t)\bigr).
\end{equation}
\end{document}