Let $G$ be a group acting on a set $A$. Then $A$ is $G$-paradoxical if there exist disjoint subsets $A_1,\dots, A_n, B_1,\dots, B_m\subset A$ and group elements $g_1,\dots,g_n,h_1,\dots,h_m\in G$ such that \(A=\bigcup_{i=1}^n g_i(A_i) \text{ and } A=\bigcup_{i=1}^m h_i(B_i).\)
Wikidata ID: Q7134470