Definition:Equidecomposable

Definition

Two sets $S, T \subset \R^n$ are said to be equidecomposable if there exists a set:

$X = \left\{{A_1, \ldots, A_m}\right\} \subset \mathcal P \left({\R^n}\right)$

where $\mathcal P \left({\R^n}\right)$ is the power set of $\R^n$, such that both $S$ and $T$ are decomposable into the elements of $X$.