Corpus ID: 117640315

Division by four

@article{Doyle2015DivisionBF,
  title={Division by four},
  author={P. Doyle and C. Qiu},
  journal={arXiv: Logic},
  year={2015}
}
  • P. Doyle, C. Qiu
  • Published 2015
  • Mathematics
  • arXiv: Logic
  • Write A<=B if there is an injection from A to B, and A==B if there is a bijection. We give a simple proof that for finite n, nA<=nB implies A<=B. From the Cantor-Bernstein theorem it then follows that nA==nB implies A==B. These results have a long and tangled history, of which this paper is meant to be the culmination. 
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