Division by four
Logic
2015-04-08 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1504.01402,
title = {Division by four},
author = {Peter G. Doyle and Cecil Qiu},
journal= {arXiv preprint arXiv:1504.01402},
year = {2015}
}