Elements of Purity (Elements in the Philosophy of Mathematics) - Tapa blanda

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9781009055895: Elements of Purity (Elements in the Philosophy of Mathematics)

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ISBN 10: 1009055895 ISBN 13: 9781009055895

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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.

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Editorial: Cambridge University Press
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ISBN 10: 1009055895
ISBN 13: 9781009055895
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Elements Of Purity

Arana, Andrew (universite De Lorraine, France)

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Arana, Andrew

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Elements of Purity (Elements in the Philosophy of Mathematics)

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Elements Of Purity

Arana, Andrew (universite De Lorraine, France)

Publicado por Cambridge University Press, 2025

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Elements of Purity (Paperback)

Andrew Arana

Publicado por Cambridge University Press, Cambridge, 2025

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Paperback. Condici�n: new. Paperback. 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. This Element explores the preference for pure proofs in mathematics since antiquity, focusing on geometry and number theory. It discusses different types of purity, reasons for preferring pure proofs, and the importance of local purity. It also touches on translation issues and the relationship between purity and local considerations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N� de ref. del art�culo: 9781009055895

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Elements of Purity

Andrew Arana

Publicado por Cambridge University Press, GB, 2025

ISBN 10: 1009055895 ISBN 13: 9781009055895

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Paperback. Condici�n: New. 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. N� de ref. del art�culo: LU-9781009055895

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