"Since the time of the ancient Greeks, when Zeno proposed his notorious paradoxes, the nature of infinity has perplexed mathematicians and philosophers. Is it a valid mathematical entity or a meaningless abstraction? Plato and Aristotle in their day, Galileo and Newton nearly two thousand years later, all grappled with it. But it was the nineteenth-century mathematicians Karl Weierstrass, Richard Dedekind, and Georg Cantor whose work established a whole new mathematics of infinity. In particular, Cantor's counterintuitive discovery of a progression of larger and larger infinities was both enormously controversial and mind-bendingly beautiful - a glimpse of a strange landscape where the everyday rules of arithmetic are broken, and where there truly can be found everything and more.". "Wallace is a splendid guide to this new territory, patiently and ingeniously taking us through the math and ideas that led to Cantor's discovery. In so doing he has created both an adept introduction to infinity and a literary masterpiece."--BOOK JACKET.