2006/05/31 by Peter G. Doyle, John Horton Conway, John H. Conway +2 · 4 voices · 1 citation
Mathematics · #Mathematics and Applications #math.CO #math.LO
paper · pdf · doi:10.48550/arxiv.math/0605779
openalex publication_date 2006/05/31 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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.