Definition:Equidecomposable

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


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

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 $$X \ $$.