How to write something underneath \min?

Question

How to type this expression, where has \min on top and \forall at the bottom?

Answer 1

The bottom part is a TeX subscript (like \sum):

\min_{\forall s \in S_j} q_k(s)

Output:

Textstyle vs. Displaystyle

Compile the following code sequence to understand the difference between textstyle and displaystyle:

\documentclass{article}
\def\sample{\min\nolimits_{\forall s \in S_j} q_k(s)}
\begin{document}
\noindent Text-Textstyle: \(\sample\)\\
          Text-Displaystyle: \(\displaystyle\sample\)
  \[
    \textrm{Text-Textstyle: }\textstyle\sample
  \]\[
    \textrm{Display-Displaystyle: }\sample
  \]
\end{document}

You can also use \nolimits and \limits to force textstyle limits and displaystyle limits respectively:

\min\limits_{\forall s \in S_j} q_k(s)