Why does \left break TeX rendering?

Question

The following TeX breaks rendering, but if I remove the \left function, the TeX renders (but without the stretchy brace). I'm helping a colleague and I'm too new to LaTeX and TeX to know how to approach fixing this.

\ \ \small{w_{1}[n] } = \left{ 
\begin{array}{ll} 
 1 & \ \ \small{n=0,1,...,12}\\
 0 & \ \ \text{otherwise} \\
\end{array}

Answer 1

You wrote \left{ <stuff>. TeX is trying to make <stuff> into a left delimiter because { opens a group. You probably meant to write \left\{ <stuff>.

Moreover, you probably should just be using the cases environment from amsmath instead.

Answer 2

Your use of the \small directive when TeX is in math mode can't work. (Moreover, the command \small is a switch and doesn't take an argument.) I suggest that you set up the MWE as follows instead:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ % begin display math
w_{1}[n]  = 
\begin{cases}
   1 & n=0,1,\dots,12\\
   0 & \text{otherwise} \\
\end{cases}
\] % end display math
\end{document}