Division by Three [PDF]
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http://math.dartmouth.edu/~doyle/docs/three/three.pdf  


John Conway, Peter Doyle  
A formal proof that it is possible to divide by three. This assertion is easy to prove using the axiom of choice, but becomes a much more difficult problem if the axiom of choice is not allowed (as is the case here). From this proof, and the much simpler proof of division by two, we know that, in general, division by any finite n is possible. Available in hypertext or PostScript. Contents include: history; the CantorSchröderBernstein theorem; division by two; subtraction; swallowing; proof of Tarski's lemma; dividing an inequality by three; division as repeated subtraction; what's wrong with the axiom of choice?; and references. PostScript and source file are available from Doyle's site.  


Levels:  College, Research 
Languages:  English 
Resource Types:  Articles 
Math Topics:  Subtraction, Graph Theory, Set Theory, Inequalities 
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