Banach-Tarski paradox

[¦bä‚näk ¦tär·skē ′par·ə‚däks] (mathematics) A theorem stating that, for any two bounded sets, with interior points in a Euclidean space of dimension at least three, one of the sets can be disassembled into a finite number of pieces and reassembled to form the other set by moving the pieces with rigid motions (translations and rotations).

Banach-Tarski paradox

(mathematics)It is possible to cut a solid ball into finitelymany pieces (actually about half a dozen), and then put thepieces together again to get two solid balls, each the samesize as the original.

This paradox is a consequence of the Axiom of Choice.

单词	banach-tarski paradox
释义	Banach-Tarski paradox Banach-Tarski paradox [¦bä‚näk ¦tär·skē ′par·ə‚däks] (mathematics) A theorem stating that, for any two bounded sets, with interior points in a Euclidean space of dimension at least three, one of the sets can be disassembled into a finite number of pieces and reassembled to form the other set by moving the pieces with rigid motions (translations and rotations). Banach-Tarski paradox (mathematics)It is possible to cut a solid ball into finitelymany pieces (actually about half a dozen), and then put thepieces together again to get two solid balls, each the samesize as the original. This paradox is a consequence of the Axiom of Choice.
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