Banach-Tarski paradox Research Papers - Academia.edu (original) (raw)
9 Followers
Recent papers in Banach-Tarski paradox
Le paradoxe de Banach-Tarski est l'un des résultats les plus surprenants des mathématiques: On se donne une boule de l'espace d'intérieur non vide. Alors, il est possible de la "découper" en un nombre fini de morceaux et de les réarranger... more
Le paradoxe de Banach-Tarski est l'un des résultats les plus surprenants des mathématiques: On se donne une boule de l'espace d'intérieur non vide. Alors, il est possible de la "découper" en un nombre fini de morceaux et de les réarranger sans les déformer pour obtenir deux boules identiques à la boule initiale à ordre près.
A premier abord, une telle duplication semble manifestement impossible. Cependant, un moment de réflexion nous rappelle que le monde mathématique n'obéit pas toujours à l'intuition.
Le but de ce document est de fournir un exposé autonome de ce paradoxe et d'introduire des sujets connexes.
This report is an overview of the Banach-Tarski paradox, from the basic steps required to prove the result up to the minimization of the number of pieces required. The paradox states that any pair of bounded non-empty sets in R3 are... more
This report is an overview of the Banach-Tarski paradox, from the basic steps required to prove the result up to the minimization of the number of pieces required. The paradox states that any pair of bounded non-empty sets in R3 are equidecomposable. A stress is placed on group and set theoretics with the results regarding paradoxical sets and groups proven generally before being applied to prove the paradox itself. I have drawn mainly upon Wagon's book, but have taken it upon myself to spell out or clarify areas in his proofs where I felt it necessary for understanding.
There is something distressing in the fact that this book, coauthored by a reputable logician, published by a reputable press and favorably reviewed by reputable reviewers, is nevertheless so marred that it cannot begin to serve its... more
There is something distressing in the fact that this book, coauthored
by a reputable logician, published by a reputable press and
favorably reviewed by reputable reviewers, is nevertheless so marred
that it cannot begin to serve its avowed purpose. The claims made by
the authors, publishers and reviewers amount to an elaborate and
cruel hoax. Where the reader is lead to expect clarity, insight and
rationality instead he finds himself in a largely indecipherable swamp
scattered with bizarre little islands of Kafkaesque puzzles and Alicein-
Wonderland meaning shifts.
We prove the Banach-Tarski decomposition paradox applied to a circle.