[BOOK] The Banach-Tarski Paradox S Wagon - 1993 - books.google ... the circle. Theorem 1.5 (AC).* St is countably SO2-paradoxical. If ... countably G-paradoxical. * In the sequel, theorems whose proof uses the Axiom of Choice will be followed by (AC). Page 28. 8 The Banach-Tarski Paradox Proof. Let M be ... Cited by 609 Related articles All 9 versions Cite Save More [PDF] from auckland.ac.nz The Banach-Tarski paradox K Stromberg - American Mathematical Monthly, 1979 - JSTOR ... s We now prove several theorems and lemmas which are of considerable interest in themselves as well as being vital stepping ... 1979] THE BANACH-TARSKI PARADOX 155 mann Theorem that any nonzero algebraic 9 will do; eg, 9= 1.) If an element pe G is expressed in its ... Cited by 73 Related articles All 3 versions Cite Save [PDF] from u-bourgogne.fr The Banach-Tarski theorem RM French - The Mathematical Intelligencer, 1988 - Springer ... one. As we have already said, our starting point will be the Hausdorff paradox. The idea ... S! Applications So we ... into balls. To produce these two copies by means of the Banach- Tarski Theorem, we need the Axiom of Choice. What ... Cited by 40 Related articles All 6 versions Cite Save Banach-Tarski theorem and Cantorian micro space-time MS El Naschie - Chaos, Solitons & Fractals, 1995 - Elsevier ... of an initial singularity at which space and time began, then all that may be needed to arrive at a four-dimensional Cantorian space-time with a Golden Mean at its core are only three theorems. ... On the initial singularity and the Banach-Tarski theorem. ... Applications and tools. ... Cited by 38 Related articles All 5 versions Cite Saved [CITATION] The Banach-Tarski paradox, volume 24 of Encyclopedia of Mathematics and its Applications S Wagon - 1985 - Cambridge University Press, … Cited by 13 Related articles Cite Save [PDF] from ams.org Banach-Tarski decompositions using sets with the property of Baire R Dougherty, M Foreman - Journal of the American Mathematical Society, 1994 - JSTOR ... S 2, and the number six is optimal; the same holds for the unit ball in Ri3 (Theorems 5.7, 5.9 ... This completes the review of the Banach-Tarski paradox and related results. We now have to see how to combine these results using arbitrary pieces with Theorem 3.1, which uses open ... Cited by 34 Related articles All 2 versions Cite Save [PS] from univ-orleans.fr [BOOK] Amenable groupoids C Anantharaman-Delaroche, J Renault - 2000 - univ-orleans.fr ... groups was initiated by J. von Neumann in 1929 in his investigation of the Banach-Tarski paradox. ... in terms of an invariant mean and Zimmers xed point property (Theorem 4.2.7 ... Among them, the study of groupoid extensions occupies an important place (Theorems 5.2.13 and ... Cited by 244 Related articles All 2 versions Cite Save More About the axiom of choice TJ Jech - Handbook of mathematical logic, 1977 - books.google ... To obtain the Banach-Tarski paradox, let us consider the following equivalence relation between sets in the three-dimensional Euclidean space: X~ Y iff ... Theorem (Banach-Tarski (1924)). ... In case of the ordering theorem, it suffices to use the finite supports mentioned in Section ... Cited by 63 Related articles All 3 versions Cite Save [PDF] from stanford.edu Mathematical Intuition Vs. Mathematical Monsters* S Feferman - Synthese, 2000 - Springer ... of the role of AC in paradoxical decompositions.18 One of the theorems they prove ... about arbitrary sets which lead one to accept the principles lying behind the paradox, namely the ... in the proof of the existence of non-measurable sets and in the Banach–Tarski theorem, one only ... Cited by 45 Related articles All 13 versions Cite Save On the uncertainty of Cantorian geometry and the two-slit experiment MS El Naschie - Chaos, Solitons & Fractals, 1998 - Elsevier ... 3. MS El Naschie; Banach-Tarski Theorem and Cantorian micro spacetime. Chaox, Solitons & Fractals, 5 (8) (1995), pp. 1503–1508. ... 4. MS El Naschie; Statistical geometry of a Cantor Discretum and semiconductors. Computers & Mathematics with Applications, 29 (12) (1995), pp ... Cited by 280 Related articles All 5 versions Cite Saved Create alert
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