Everything and More: A Compact History of Infinity
One of the outstanding voices of his generation, David Foster Wallace has won a large and devoted following for the intellectual ambition and bravura style of his fiction and essays. Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.
Other editions - View all
abstract actually analysis Aristotle Aristotle's arithmetic Axiom Axiom of Choice basic bers Bolzano calc calculus Cantor Cantorian cardinal number Cauchy college math concept continuous continuous function Continuum Continuum Hypothesis convergent convergent series correspondence curve Dauben decimal Dedekind defined definition denumerable derived set Dichotomy entities Eudoxus example exist finite formal Fourier Series function Galileo geometric Georg Cantor Gödel going Greek idea important impredicative infinite number infinite sequence infinite sets infinitesimals infinity integers interval involves irrational numbers kind Kline Kronecker Leibniz limit logical math's mathematical mathematicians means metaphysical nite Number Line order-types ordinal paradoxes problems proof prove quantities rational numbers Real Line real numbers recall reductio relation rigorous schnitt semicribbed sense set theory sort stuff subsets symbol technical Theorem there's thing tions transfinite transfinite math transfinite numbers trig series true Weierstrass Weierstrassian whole Zeno Zeno's Zeno's Paradoxes