Curly brace error occurring when curly braces are closed correctly

Question

As title says I get error:

line 55: Missing { inserted ... $$\sum_{i=1}^{n} \lambda_i v_i =O_\vec{E}
line 55: Missing } inserted ...v_n \in A =>\lambda_i =0,...,\lambda_n =0$
: Not defining \perthousand.
: Not defining \micro.

The exact line and its context are:

 \begin{itemize} 
     \item On dit que A est \textit{libre} si le seule c. l. de vecteurs de A egales a $O_E$ est la c. l. triviale.
     \item C'est-a-dire si: 
$$\sum_{i=1}^{n} \lambda_i v_i =O_\vec{E}, v_1...v_n \in A =>\lambda_i =0,...,\lambda_n =0$$
\end{itemize}

The packages I have imported are:

\usepackage[utf8]{inputenc}
\usepackage{gensymb}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{fancyhdr}
\usepackage[margin=.75in, a4paper, portrait]{geometry}

Answer 1

The problem here stems from the somewhat greedy nature of the subscript routine when you use

O_\vec{E}

It grabs \vec without it's argument giving rise to the problem. Here are my suggestions to fix your situation:

• Don't use $$...$$. Instead, use \[...\] (see Why is \[ … \] preferable to $$ … $$?);
• Ellipsis are defined in LaTeX; with amsmath you can use smart \dots;
• Relations should be used, so \implies (say) instead of =>

Here is a complete minimal example:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{itemize} 
  \item Here is some \textit{regular} text, mixed in with $O_E$ some math.
  \item And a display equation:
    \[
      \sum_{i=1}^{n} \lambda_i v_i 
        = O_{\vec{E}}, v_1,\dots,v_n \in A 
        \implies \lambda_i = 0,\dots,\lambda_n 
        = 0
    \]
\end{itemize}

\end{document}