# 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 finitely
many pieces (actually about half a dozen), and then put the
pieces together again to get two solid balls, each the same
size as the original.

This paradox is a consequence of the Axiom of Choice.

This paradox is a consequence of the Axiom of Choice.

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page: