@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}
}

{"_id":"Sq9D37id2T9GAE9ZX","bibbaseid":"doyle-conway-divisionbythree","authorIDs":[],"author_short":["Doyle, P. G.","Conway, J. H."],"bibdata":{"bibtype":"article","type":"article","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":[{"propositions":[],"lastnames":["Doyle"],"firstnames":["Peter","G."],"suffixes":[]},{"propositions":[],"lastnames":["Conway"],"firstnames":["John","Horton"],"suffixes":[]}],"file":"/home/dimitri/Nextcloud/Zotero/storage/GIR879I2/Doyle and Conway - 2006 - Division by three.pdf;/home/dimitri/Nextcloud/Zotero/storage/UZJYUJPP/0605779.html","bibtex":"@article{doyleDivisionThree2006,\n archivePrefix = {arXiv},\n eprinttype = {arxiv},\n eprint = {math/0605779},\n title = {Division by Three},\n url = {http://arxiv.org/abs/math/0605779},\n 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.},\n urldate = {2019-03-03},\n date = {2006-05-31},\n keywords = {Mathematics - Combinatorics,Mathematics - Logic,03E10 (Primary),03E25 (Secondary)},\n author = {Doyle, Peter G. and Conway, John Horton},\n file = {/home/dimitri/Nextcloud/Zotero/storage/GIR879I2/Doyle and Conway - 2006 - Division by three.pdf;/home/dimitri/Nextcloud/Zotero/storage/UZJYUJPP/0605779.html}\n}\n\n","author_short":["Doyle, P. G.","Conway, J. H."],"key":"doyleDivisionThree2006","id":"doyleDivisionThree2006","bibbaseid":"doyle-conway-divisionbythree","role":"author","urls":{"Paper":"http://arxiv.org/abs/math/0605779"},"keyword":["Mathematics - Combinatorics","Mathematics - Logic","03E10 (Primary)","03E25 (Secondary)"],"downloads":0},"bibtype":"article","biburl":"https://raw.githubusercontent.com/dlozeve/newblog/master/bib/all.bib","creationDate":"2020-01-08T20:39:39.276Z","downloads":0,"keywords":["mathematics - combinatorics","mathematics - logic","03e10 (primary)","03e25 (secondary)"],"search_terms":["division","three","doyle","conway"],"title":"Division by Three","year":null,"dataSources":["3XqdvqRE7zuX4cm8m"]}