巴拿赫-塔斯基悖论

100 Years of Math Milestones Pub Date : 2019-06-12 DOI:10.1090/mbk/121/12

D. Raman

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引用次数: 0

摘要

数学，在其最早的形式中，是一系列用于量化、建模和理解我们周围世界的方法。然而，随着对这一古老学科的研究不断深入，它已经演变成一个独立的宇宙，虽然深刻而美丽地触动了我们自己，但它是一个从根本上不同的实体，是从我们的抽象思想中创造出来的。正如阿尔伯特·爱因斯坦在他的《相对论的旁注》中优雅地指出的那样:“就数学定律与现实的关系而言，它们是不确定的;就它们所确定的而言，它们并不是指现实。”这篇文章写于1922年，比《BAN24》发表早两年，《BAN24》证明了巴拿赫-塔斯基悖论，这是这句话最引人注目的例子之一。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Banach–Tarski paradox

for 28 Mar 2013 In 1924, Banach and Tarski proved that any bounded solid region in 3-space can be decomposed into finitely many pieces that can be rearranged using Euclidean isometries to produce any other bounded solid region desired. As it is often put, "a pea can be chopped up and reassembled to produce the sun." I will present this paradoxical result and discuss the extent to which the Axiom of Choice can be blamed for it.

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