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The word 'infinity' usually elicits feelings of awe, wonder, and admiration; the concept infinity has fascinated philosophers and theologians. The author shows how professional mathematicians tame this unwieldy concept, come to terms with it, and use its various aspects as their most powerful tools of the trade. The early chapters are descriptive and intuitive, full of examples that not only illustrate some infinite processes, but that are worth studying for their own sake. Many questions are raised in the beginning, partially answered in various contexts throughout the book, and finally treated with the precision necessary to give the reader an excellent grasp of the fundamental notions used in the calculus as well as in virtually all other mathematical disciplines. The text is peppered with challenging problems whose solutions appear at the end of the book.

Processes, Infinite. --- Infinite.

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SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity , international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

Infinite --- Infinity --- Finite, The

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Inequalities (Mathematics) --- Processes, Infinite

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"Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame.

Series, Infinite. --- Mathematics --- Math --- Science --- Infinite series --- Philosophy --- History.

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This book constitutes the proceedings of the 2000 Howard conference on "Infinite Dimensional Lie Groups in Geometry and Representation Theory". It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and esta

Infinite dimensional Lie algebras --- Infinite groups --- Infinite-dimensional manifolds --- Lie groups