[Tex/LaTex] Creating curly braces with limits

Question

Hello, I am trying to create curly braces with lower and upper limits to the right, as shown in the picture. I am unable to fix these limits on the braces. I am using \bigl\{ and \bigr\} to create the braces.

Answer 1

For me the standard way works. Have you tried this?

\documentclass[]{article}

\usepackage{amsmath}

\begin{document}
Thus, we get
\[
  \bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n
\]
and
\[
  \bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n
\]

In the same line:
\[
  \bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n
  \quad\text{and}\quad
  \bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n
\]

This is a long line, so that the equations are in the middle of two lines.
Everything in the same line using inline $\bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n$
and $\bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n$. But this doesn't look good, because
it might stretch the linespacing.

Using 
\[
  \text{Thus, we get}\quad%
  \bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n
  \quad\text{and}\quad
  \bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n
\]
does look better for the line spacing, but honestly it is not that pretty, imho.
\end{document}