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Andrew Arana
Elements of Purity
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7266252Elements of Purityhttps://www.gandhi.com.mx/elements-of-purity-9781009059572/phttps://gandhi.vtexassets.com/arquivos/ids/6817229/image.jpg?v=638738175716830000365445MXNCambridge University PressInStock/Ebooks/<p>A proof of a theorem can be said to be pure if it draws only on what is close or intrinsic to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.</p>...6906855Elements of Purity365445https://www.gandhi.com.mx/elements-of-purity-9781009059572/phttps://gandhi.vtexassets.com/arquivos/ids/6817229/image.jpg?v=638738175716830000InStockMXN99999DIEbook20259781009059572_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_<p>A proof of a theorem can be said to be pure if it draws only on what is close or intrinsic to that theorem. In this Element we will investigate the apparent preference for pure proofs that has persisted in mathematics since antiquity, alongside a competing preference for impurity. In Section 1, we present two examples of purity, from geometry and number theory. In Section 2, we give a brief history of purity in mathematics. In Section 3, we discuss several different types of purity, based on different measures of distance between theorem and proof. In Section 4 we discuss reasons for preferring pure proofs, for the varieties of purity constraints presented in Section 3. In Section 5 we conclude by reflecting briefly on purity as a preference for the local and how issues of translation intersect with the considerations we have raised throughout this work.</p>...9781009059572_Cambridge University Presslibro_electonico_9781009059572_9781009059572Andrew AranaInglésMéxicohttps://getbook.kobo.com/koboid-prod-public/cambridgeupress-epub-c7a1655f-967e-4cf5-a3db-bce6891db492.epub2025-01-16T00:00:00+00:00Cambridge University Press