# Division by three

- Published in 2006
- Added on

In the collection

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.

## Links

### BibTeX entry

@article{Doyle2006, title = {Division by three}, author = {Doyle, Peter G. and Conway, John Horton}, url = {https://arxiv.org/abs/math/0605779v1 https://arxiv.org/pdf/math/0605779v1.pdf}, urldate = {2014-11-17}, 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.}, comment = {}, month = {may}, year = 2006, collections = {Fun maths facts} }