Division by Three

Division by Three. Doyle, P. G. and Conway, J. H.

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.

@article{doyleDivisionThree2006,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {math/0605779},
  title = {Division by Three},
  url = {http://arxiv.org/abs/math/0605779},
  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.},
  urldate = {2019-03-03},
  date = {2006-05-31},
  keywords = {Mathematics - Combinatorics,Mathematics - Logic,03E10 (Primary),03E25 (Secondary)},
  author = {Doyle, Peter G. and Conway, John Horton},
  file = {/home/dimitri/Nextcloud/Zotero/storage/GIR879I2/Doyle and Conway - 2006 - Division by three.pdf;/home/dimitri/Nextcloud/Zotero/storage/UZJYUJPP/0605779.html}
}

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