# 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

## Other information

- key
- Doyle2006
- type
- article
- date_added
- 2014-11-17
- date_published
- 2006-05-01

### BibTeX entry

@article{Doyle2006, key = {Doyle2006}, type = {article}, title = {Division by three}, author = {Doyle, Peter G. and Conway, John Horton}, 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 = {}, date_added = {2014-11-17}, date_published = {2006-05-01}, urls = {https://arxiv.org/abs/math/0605779v1,https://arxiv.org/pdf/math/0605779v1.pdf}, collections = {Fun maths facts}, url = {https://arxiv.org/abs/math/0605779v1 https://arxiv.org/pdf/math/0605779v1.pdf}, urldate = {2014-11-17}, month = {may}, year = 2006 }