Missing { and } inserted

pdflatex keeps complaining about braces but they are balanced. I read that some environments start math mode automatically, but I don't think I'm using them.

Here is the code:

\documentclass{article}

\title{Analisi I - Teoremi}
\date{\today}
\usepackage{amsthm}

\begin{document}
\maketitle
\newpage

\section{Limit Infiniti}
\newtheorem*{perm}{Teorema della permanenza del segno}
\begin{perm}
Sia $\lim_\limits{x \to \alpha} f(x) = +\infty$ e $a > 0$. Allora esiste
una semiretta su cui $f(x) > a > 0$.
\end{perm}
\begin{proof}
Segue immediatamente dalla definizione. \qedhere
\end{proof}

\newtheorem*{confronto}{Teorema del confronto}
\begin{confronto}
Sia $\lim_\limits{x \to \alpha} f(x) = +\infty$ e $g(x) \geq f(x)$. Allora
$\lim_\limits{x \to \alpha} g(x) = +\infty$.
\end{confronto}
\begin{proof}
\$\begin{cases} f(x) &> \epsilon\\ g(x) &\geq f(x) \end{cases} \implies g(x) > \epsilon \$
\end{proof}
% section Limit Infiniti (end)

\end{document}
• @HarishKumar Unfortunately the problem persists. Feb 1 '15 at 14:49

This is what went wrong:

1. You didn't load amsmath but used cases.
2. \lim_\limits{x... should be \lim\limits_{x.. i.e, _ should come after \limits not before.
3. You have used \$....\$ for display equation which should be $....$

Corrected code:

\documentclass{article}
\usepackage{amsmath}

\title{Analisi I - Teoremi}
\date{\today}
\usepackage{amsthm}

\begin{document}
\maketitle
\newpage

\section{Limit Infiniti}
\newtheorem*{perm}{Teorema della permanenza del segno}
\begin{perm}
Sia $\lim\limits_{x \to \alpha} f(x) = +\infty$ e $a > 0$. Allora esiste
una semiretta su cui $f(x) > a > 0$.
\end{perm}
\begin{proof}
Segue immediatamente dalla definizione. \qedhere
\end{proof}

\newtheorem*{confronto}{Teorema del confronto}
\begin{confronto}
Sia $\lim\limits_{x \to \alpha} f(x) = +\infty$ e $g(x) \geq f(x)$. Allora
$\lim\limits_{x \to \alpha} g(x) = +\infty$.
\end{confronto}
\begin{proof}
$\begin{cases} f(x) > \epsilon\\ g(x) \geq f(x) \end{cases} \implies g(x) > \epsilon$
\end{proof}
% section Limit Infiniti (end)

\end{document}

The format for cases is

<case> & <condition>

and since you don't have any conditions here, no need of using & here and f(x) > \epsilon gives proper spacing.

• Great, thanks for your help. I forgot about amsmath Feb 1 '15 at 14:57