Essays about: "Banach-Tarski"

Found 2 essays containing the word Banach-Tarski.

  1. 1. The Banach-Tarski paradox

    University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

    Author : Carl Elofsson; Adrian Nilsson; Nicolas Söderberg; Tim Westlund; [2022-07-04]
    Keywords : ;

    Abstract : In this thesis we present a proof of the Banach-Tarski paradox, a counterintuitive result that states that any ball in R3 can be cut into finitely many pieces and then be reassembled into two copies of the original ball. Since the result follows from the axiom of choice it is important for assessing its role as an axiom of mathematics. READ MORE

  3. 2. The Banach-Tarski Paradox : How I Learned to Stop Worrying and Love the Axiom of Choice

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Mats Karl Anders Wahlberg; [2022]
    Keywords : Banach; Tarski; Banach-Tarski; Banach-Tarski paradox; Hausdorff; Hausdorff paradox; paradox; measure; measure theory; axiom of choice; Banach; Tarski; Banach-Tarski; Banach-Tarskis paradox; Hausdorff; Hausdorffs paradox; paradox; mått; måtteori; urvalsaxiomet; valaxiomet;

    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. READ MORE