\begin{definition}[Definition:Equidecomposable]
Two sets $S, T \subset \R^n$ are said to be '''equidecomposable''' if there exists a set:
:$X = \set {A_1, \ldots, A_m} \subset \powerset {\R^n}$
where $\powerset {\R^n}$ is the power set of $\R^n$, such that both $S$ and $T$ are decomposable into the elements of $X$.
\end{definition}