| 释义 |
Banach-Tarski paradox A solid three-dimensional sphere can be partitioned into five sets which can be moved using isometries and reassembled to create two identical solid spheres. The result is paradoxical, as it seems volume ought to be an invariant of the process, but the five parts are not measurable and cannot be assigned volumes themselves. The paradox cannot be proved using the Zermelo-Fraenkel axioms but is true assuming the axiom of choice.
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