INFINITY

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