Who has not wondered if there is something beyond the universe? Or if there is a biggest number? Or if there is something smaller than the smallest thing? These are questions about different infinities. Exploring the paradoxes and riddles of what infinity means is the invitation contained in this book. This classic book, written by the seminal Leapfrogs team, has been visually updated in this second edition for a new generation. A great addition to any mathematician's library - and to school and public libraries too.
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Ray Hemmings and Dick Tahta were pre-eminent mathematics educators in the late Twentieth Century, and formed the Leapfrogs Group to produce a range of excellent resources and to explore ideas. Alf Coles was part of this Group.
"Anyone, young or old, with any interest in mathematics will at some point have been fascinated by the ideas of paradox and of infinity. This book was first published by Tarquin Books famous for its production of mathematical paper kits for polyhedra constructions and much else. This present edition is published by the Leapfrogs Group. The book is famous for the way that it blends text with illustrative diagrams. It starts with the ideas concerning recursion and works through to the ideas concerning paradox and Cantor's sets and the notion of "infinities of infinity". Examples of topics well described and illustrated are: Zeno's and Galileo's paradoxes, mathematical series, number theory, snowflakes and fractals, prime number theory, nesting, tessellation, Mandelbrot and Cantor sets and (Hebrew) Aleph, correspondence and countability, and much more. "Infinite sets are not like finite sets - in an infinite set you can have a part of it which is equal the the whole of it". All who finds mathematical ideas exciting, will be delighted with this book. I have used the book for many years both for teaching and personal interest. I have seen no other general book that treats infinity so well." K Sharratt, Teacher
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