„Banach–Tarski-paradoxon” változatai közötti eltérés

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kozmetikai javítások
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'''Step 1.''' The free group with two generators ''a'' and ''b'' consists of all finite strings that can be formed from the four symbols ''a'', ''a''<sup>-1</sup>, ''b'' and ''b''<sup>-1</sup> such that no ''a'' appears directly next to an ''a''<sup>-1</sup> and no ''b'' appears directly next to a ''b''<sup>-1</sup>. Two such strings can be concatenated and converted into a string of this type by repeatedly replacing the "forbidden" substrings with the empty string. For instance: ''abab''<sup>-1</sup>''a''<sup>-1</sup> concatenated with ''abab''<sup>-1</sup>''a'' yields ''abab''<sup>-1</sup>''a''<sup>-1</sup>''abab''<sup>-1</sup>''a'', which gets reduced to ''abaab''<sup>-1</sup>''a''. One can check that the set of those strings with this operation forms a group with neutral element the empty string <math>e</math>. We will call this group <math>F_2</math>.
 
 
[[Kép:Paradox felbontás F2.png|thumb|right|250px|A ''S''(''a''<sup>-1</sup>) halmaz és a ''aS''(''a''<sup>-1</sup>) halmaz ''F''<sub>2</sub>-nek a [[Cayley ábra]]ján]]
* Beke Tibor: [http://www.sulinet.hu/cgi-bin/db2www/lm/komal/cikk?id=198917&l= Hogyan csináljunk aranyat, avagy a Banach-Tarski paradoxonról], ''Középiskolai Matematikai Lapok'', 1989/11
* Laczkovich Miklós: ''Sejtés és bizonyítás'', Typotex, 1998, ISBN 9637546898
* Stan Wagon: ''The Banach-Tarski Paradox'', Encyclopedia of Mathematics and its Applications, <b>'''24</b>''', 1985.
* Leonard M. Wapner: ''The pea and the sun'', A K Peters, 2005. ISBN 1 56881 213 2
 
 
[[Kategória:Paradoxonok]]
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