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. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

"This particular volume does exactly what it says on the tin, providing just enough background on various aspects of infinity to pique the readers interest. It is written with the same clarity and attention to detail as Professor Stewarts other books." - David Hopkins, Mathematical Gazette

"Stewart has turned what must have seemed like a daunting project into an entertaining, illuminating, and digestible read... the book has something for everyone." - Marianne Freiberger, Plus

"Even the experienced reader may have more occasion to learn something new. Some of these non-essential but nevertheless flashes of a that's-interesting-I-didn't-know-that experience will make it worthwhile reading." - Adhemar Bultheel, European Mathematical Society