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Posted on: Thursday, February 04, 2010 7:04 PM
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Subject: Math_Division by 3
| Division by three Peter G. Doyle John Horton Conway ∗ Version dated 1994 GNU FDL† Abstract We prove without appeal to the Axiom of Choice that for any sets A and B, if there is a one-to-one correspondence between 3 × A and 3 × B then there is a one-to-one correspondence between A and B. The first such proof, due to Lindenbaum, was announced by Lindenbaum and Tarski in 1926, and subsequently 'lost'; Tarski published an alternative proof in 1949. We argue that the proof presented here follows Lindenbaum's original. AMS Classification numbers ondary). 03E10 (Primary); 03E25 (Sec- 1 Introduction |
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