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Infinity (Mathematics)
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Infinity
ISBN: 9780198755234
Series: A Very Short Introduction
Infinity (Mathematics)
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ISBN
9780198755234 (10-digit ISBN: 0198755236)
- Description
- Key Features
- Series Description
- Table of Contents
- Explains the mathematical concept of infinity and its uses in calculus, Fourier analysis, and fractals
- Discusses the role of infinity in the physics of space, time, and matter
- Describes philosophical aspects and debates involving infinity, and shows how current mathematical thinking can be used to illuminate some of those issues.
- Considers the important applications of the concept of infinity to everyday reality
Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.
Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible.
Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library.
Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.
Please note: As this series is not ELT material, these titles are not subject to discount.
Introduction
1: Why infinity is dangerous
2: The flipside of infinity
3: Geometric infinity
4: Infinity in probability
5: Physical infinity
6: Counting infinity
7: Infinity revisited
References
Further Reading
Index
Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.
Key Features
- Explains the mathematical concept of infinity and its uses in calculus, Fourier analysis, and fractals
- Discusses the role of infinity in the physics of space, time, and matter
- Describes philosophical aspects and debates involving infinity, and shows how current mathematical thinking can be used to illuminate some of those issues.
- Considers the important applications of the concept of infinity to everyday reality
Series Description
Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible.
Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library.
Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.
Please note: As this series is not ELT material, these titles are not subject to discount.
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