Revision #719 → #1029 · back to history
addedBanach–Tarski paradox4d7a390f4cdf
addedPea and the Sun paradox (alternative form)9c1dbb828846
addedContinuous motion of pieces (2005)c5b25cfa9e91
addedLocale-theoretic resolution (Leroy–Simpson)0a525da2532c
addedStrong form of the Banach–Tarski paradoxcb74bac43b29
addedDoubling a ball via translated copiesa40994554f96
addedCountable analogue in dimensions 1 and 2e1e966a92569
addedTarski's characterization of amenable groupsceb51118a7b2
addedCongruent figures under G-actionf3e265d33926
addedG-equidecomposable setsc167beb4d943
addedParadoxical setb82eb31693a2
addedReformulation of Banach–Tarski paradox1a7000c5baf0
addedRobinson's five-piece sharp result83446b0a61a7
addedStrong version of the paradoxb85a113dc5f9
addedBanach's Bernstein–Schroeder generalizationbac5410abffe
addedNonexistence of invariant finitely additive measure9af0db2b0bf7
addedConverse: paradox-free implies invariant measure086141daf85c
addedHausdorff paradox0562d80759b6
addedNon-equidecomposability of nested Euclidean polygons14a0f206ab81
addedMorse: polygon result provable in ZF8653ad83654b
addedCohen: independence of AC from ZFfde411a50e1b
addedBanach–Tarski not provable in ZF+DCcae969845fbf
addedPawlikowski: paradox from ZF + Hahn–Banach6113b094a195
addedFree group F_2 on two generators095716b822c9
addedString reduction in F_28ef4f36bf12b
addedParadoxical decomposition of F_2ad3ae8194cb0
addedFree rotation group H isomorphic to F_258b5edd3994b
addedFailure in two dimensions4fd6d2e40493
addedQuaternion proof of free rotation subgroups94b3184e8752
addedParadoxical decomposition of the sphere S^2e00d3e0fb7c9
addedDecomposition of solid ball minus center2d10f8829d92
addedS^2 − D equidecomposable with S^2841b545a14af
addedBall minus a point equidecomposable with ball61ec9b4d73f8
addedTransitivity of equidecomposability2d4c0e65a939
addedFive pieces is best possibledfa84ccd05ea
addedk copies of a ball in n-spacef5c50b788f57
addedContinuum-many-piece partition of S^{n−1}854d442a7c4a
addedVon Neumann's paradox in the planee6fae01b0ef9
addedLaczkovich's SL(2,R) paradoxical decompositiond8b393733fb0
addedSatô: four pieces suffice for SA_2ce5b60f5beb1
addedTomkowicz: free piecewise linear group on punctured disk8af8664e84d9
addedAdams–Mycielski fractional parts of S^24d2e20c1d206
addedTomkowicz: generalization to hyperbolic plane43223110dd7e
addedBanach–Tarski paradox in hyperbolic plane99736679d354
addedMycielski–Wagon Borel paradox in H^203fb3c1c7fa8
addedTomkowicz: free discontinuous subgroup of SA(3,Z)8cf91160725d
addedCountable equidecomposability via Lebesgue pieces44019ed37bff
addedExtension to Lie and locally compact groupsde5e0f42b28c
addedColoring rule linking paradoxes and optimization929694411301
addedGenericity of bounded paradoxical sets322cfb6d1cb4