[Tex/LaTex] Help with a displayed formula with a determinant

Question

\begin{center}
$
 \delta = 
 \left|
\begin{array}{cc} 
1 & x_{0} & x_{0}^{2} & ... & x_{0}^{n} \\ 
1 & x_{1} & x_{1}^{2} & ... & x_{1}^{n} \\
............................ \\
1 & x_{n} & x_{n}^{2} & ... & x_{n}^{n} \\ 
\end{array}
\right|

 = {\displaystyle \prod_{0\leq j < i \leq n} (x_{i} - x_{j})} $
\end{center}

It does not work! How can I do that \delta = Vandermond Determinant = \prod?

Answer 1

Remove the blank line, which is not allowed in math environments. Also you're defining an array with two columns and use five of them.

However you're not using the right tools: for a displayed equation use \[...\] and not center.

\documentclass{article}
\usepackage{amsmath} % always load it for math

\begin{document}

\[
\delta =
\begin{vmatrix}
1 & x_{0} & x_{0}^{2} & \dots & x_{0}^{n} \\ 
1 & x_{1} & x_{1}^{2} & \dots & x_{1}^{n} \\
\hdotsfor{5} \\
1 & x_{n} & x_{n}^{2} & \dots & x_{n}^{n}
\end{vmatrix}
=
\prod_{0\leq j < i \leq n} (x_{i} - x_{j})
\]

\end{document}