[Tex/LaTex] Brackets around multiple lines

bracketsmath-mode

I am trying to put big rounded brackets around some text that contains math formulas:

Jede Teilfolge hat entweder unendliche viele Elemente von $\left( g_{2n}\right)$ oder $\left( g_{2n+1}\right)$.\todo{Add big bracket}
\[\left. {\begin{array}{*{20}{c}}
{{g_ + } = \lim {a_n} = \lim {g_{2n}} = g}\\
{{g_ + } = \lim {b_n} = \lim {g_{2n}} = g}
\end{array}} \right\}{g_ + } = {g_ - } \Rightarrow \lim {g_n} = g = {g_ - } = {g_ + } = \frac{{1 + \sqrt 5 }}{2}\]

The result that I am looking for is something along these lines:

( First Line  )
( Second Line )
( Third Line  )

All of the solutions that I have found force me to go into mathmode, clashing with the formulas, or they use tikz in an enumerated list, which I haven't been able to adapt to my situation.

Thanks in advance for your help!

EDIT: Looks like I didn't explain myself too well. Here something I sketched up, hope this explains it better:
quickMockup

Of course the brackets should be as tall as the text, and not go over like in my sketch

Best Answer

You need the rcases or drcases environment from mathtools:

\documentclass{article}
\usepackage{mathtools}

\begin{document}

Jede Teilfolge hat entweder unendliche viele Elemente von $(g_{2n})$ oder
$(g_{2n+1})$.
\[
\begin{drcases}
g_+ = \lim a_n = \lim g_{2n} = g\\
g_+ = \lim b_n = \lim g_{2n} = g
\end{drcases}
g_+ = g_- \Rightarrow \lim g_n = g = g_- = g_+ = \frac{1 + \sqrt{5}}{2}
\]

\end{document}

Note that you're using too many braces; also there's no need to have \left or \right before all delimiters: it's even discouraged, as it affects spacing.

Usually I also recommend to always have braces around subscripts and superscripts, even if they are only one token, but an experienced user knows when to sin against this “rule”.

enter image description here

I wouldn't use brackets around the whole construction, but the document is yours; here is how you can do it:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum} % just for the example
\newsavebox{\tempbox}

\begin{document}
\lipsum*[2]
\[
\sbox{\tempbox}{%
  $\displaystyle
    \begin{drcases}
    g_+ = \lim {a_n} = \lim g_{2n} = g\\
    g_+ = \lim {b_n} = \lim g_{2n} = g
    \end{drcases} 
    g_+ = g_- \Rightarrow \lim g_n = g = g_- = g_+ = \frac{1 + \sqrt{5}}{2}
  $%
}
\begin{pmatrix}
\,\parbox[b]{\wd\tempbox}{
  Jede Teilfolge hat entweder unendliche viele Elemente von
  $(g_{2n})$ oder $(g_{2n+1})$.
}\hfill\, % left alignment
\\[\abovedisplayskip]
\,\usebox{\tempbox}\,
\end{pmatrix}
\]
\lipsum[3]
\end{document}

enter image description here

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