Infinity: A Very Short IntroductionInfinity 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. |
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Isi
| 1 | |
| 8 | |
| 19 | |
| 32 | |
| 54 | |
Geometric infinity | 70 |
| 91 | |
Counting infinity | 103 |
References | 131 |
Further reading | 133 |
Publishers acknowledgements | 137 |
Index | 139 |
Very Short Introduction | 144 |
Istilah dan frasa umum
Achilles actual infinity algebraic numbers analysis argument Aristotle Aristotle’s arithmetic artist balls calculus Cantor Chapter circle complex concept construction continuum Continuum Hypothesis corresponding curvature David defined definition diagonal digits distinction Euclid’s geometry Euclidean geometry Euclidean plane exactly example exist Figure finite forever function googol grid Hilbert’s hotel Hippasus horizon idea infinite decimal infinite number infinite sets infinitesimal integers interval John largest number Leibniz length light limit line at infinity logical match mathematicians mathematics meet Michael natural numbers non-standard analysis notation number system object one-to-one ordinals paradox parallel lines perspective Peter philosophical physical point at infinity positive number potential infinity projective proof properties proved quantity radius rainbow angle rational numbers ray optics real numbers recurring decimal sense sequence set theory sheep singularity smaller space specific square theorem there’s today’s tortoise transcendental numbers transfinite cardinals triangle universe whole numbers Zeno’s zero ℵ ℵ ℵ
Informasi bibliografi
| Judul | Infinity: A Very Short Introduction Volume 519 dari Very short introductions |
| Pengarang | Ian Stewart |
| Edisi | berilustrasi |
| Penerbit | Oxford University Press, 2017 |
| ISBN | 0198755236, 9780198755234 |
| Tebal | 143 halaman |
| Ekspor Kutipan | BiBTeX EndNote RefMan |