Content deleted Content added
m Added link |
Dab |
||
Line 5:
==Definition==
Suppose a group <math>G</math> acts on a set <math>A</math>. Then <math>A</math> is <math>G</math>-paradoxical if there exists some disjoint subsets <math>A_1,...,A_n,B_1,...,B_m \subseteq A</math> and some group elements <math>g_1,...,g_n,h_1,...,h_m \in G</math> such that:<ref>{{cite book|last1=Wagon|first1=Stan|last2=Tomkowicz|first2=Grzegorz|title=The Banach–Tarski Paradox|title-link= The Banach–Tarski Paradox (book)|date=2016|isbn=978-1-107-04259-9|edition=Second}}</ref>
<math>A = \bigcup_{i=1}^n g_i(A_i)</math> and <math>A = \bigcup_{i=1}^m h_i(B_i)</math>
| |||