The Banach-Tarski Paradox
History and Overview
2022-06-29 v1 Combinatorics
Functional Analysis
Abstract
This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical significance of the paradox for measure theory is covered, along with its incorrect attribution to Banach and Tarski. Finally, the necessity of the axiom of choice is discussed and contrasted with other axiomatic and topological assumptions that enable the paradoxes.
Keywords
Cite
@article{arxiv.2206.13512,
title = {The Banach-Tarski Paradox},
author = {Mats Wahlberg},
journal= {arXiv preprint arXiv:2206.13512},
year = {2022}
}
Comments
55 numbered pages, 61 total pages