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arXiv:1504.01402math.LO

Division by four

Peter G. Doyle, Cecil Qiu

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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.

arXiv comments
Journal reference
DOI
Subjects
math.LOLogic math.COCombinatorics

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  1. Division by three (2006) 1 comment

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