Infinity: A Very Short Introduction

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.

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.

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

"... a concise and compelling invitation to think about some of the deeper issues behind basic questions about infinity ... Written in an accessible style, yet not skirting ideas of convergence or an occasional proof by contradiction, Infinity should appeal to a broad audience of math fans. I would
especially recommend the book as supplementary reading for students of calculus or introductory set theory and to anybody who has ever found themselves baffled or awed by the mysteries of infinity." -- Briana Foster-Greenwood, Mathematical Association of America