\begin{definition}[Definition:Interval of Convergence]
Let $\xi \in \R$ be a real number.
Let $\ds \map S x = \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$ be a power series in $x$ about $\xi$.
Then the set of values of $x$ for which $\map S x$ converges is called the '''interval of convergence''' of $S$.
\end{definition}