A Continuous Movement Version of the Banach-Tarski Paradox: A Solution to de Groot's Problem

Journal of Symbolic Logic 70 (3):946 - 952 (2005)
Abstract
In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B. i.e., a piecewise isometry from B onto two copies of B. This article answers a question of de Groot from 1958 by showing that there is a paradoxical decomposition of B in which the pieces move continuously while remaining disjoint to yield two copies of B. More generally, we show that if n ≥ 2, any two bounded sets in Rⁿ that are equidecomposable with proper isometries are continuously equidecomposable in this sense
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Patrick Greenough (2011). Truthmaker Gaps and the No-No Paradox. Philosophy and Phenomenological Research 82 (3):547 - 563.
    Arianna Betti (2004). Lesniewski's Early Liar, Tarski and Natural Language. Annals of Pure and Applied Logic 127 (1-3):267-287.
    Chris Freiling (1984). Banach Games. Journal of Symbolic Logic 49 (2):343-375.
    Dale Jacquette (2010). Circularity or Lacunae in Tarski's Truth-Schemata. Journal of Logic, Language and Information 19 (3):315-326.
    José Iovino (1999). Stable Models and Reflexive Banach Spaces. Journal of Symbolic Logic 64 (4):1595-1600.
    Analytics

    Monthly downloads

    Added to index

    2010-08-24

    Total downloads

    6 ( #162,810 of 1,088,427 )

    Recent downloads (6 months)

    0

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.