KnowraBanach–Tarski paradoxLinked fromLinked fromThe 11 pages that link to Banach–Tarski paradox, each with the reason it gives.All 11Broader topic 6Related 3Compared with 2Axiom of choiceBroader topic: It exposes a counterintuitive consequence of allowing nonconstructive selections.Well-ordering theoremBroader topic: Its proof uses choice, whose equivalent well-ordering principle underwrites highly nonconstructive selections.Choice functionBroader topic: Its proof depends on choice principles that permit highly nonconstructive selections.InfinityBroader topic: This counterintuitive result exposes consequences of infinite decompositions and the axiom of choice.Nonmeasurable setBroader topic: Its finite pieces are nonmeasurable, preventing ordinary volume from being preserved across the decomposition.Hausdorff paradoxBroader topic: It strengthens the sphere result by producing two balls from one using finitely many pieces.