Interesting Esoterica

Division by three

Article by Doyle, Peter G. and Conway, John Horton
  • Published in 2006
  • Added on
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 cross A and 3 cross 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.

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BibTeX entry

@article{Doyle2006,
	title = {Division by three},
	author = {Doyle, Peter G. and Conway, John Horton},
	url = {https://arxiv.org/abs/math/0605779v1 https://arxiv.org/pdf/math/0605779v1.pdf},
	urldate = {2014-11-17},
	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 cross A and 3 cross 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.},
	comment = {},
	month = {may},
	year = 2006,
	collections = {}
}