Everything and More: A Compact History of InfinityOne 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 nineteenthcentury 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 highprofile recognition to the bizarre and fascinating world of higher mathematics. 
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David Foster Wallace was a great writer of fiction.  Goodreads
This I credit to DFW's writing style.  Goodreads
This wants to be a pop intro to the concept of history.  Goodreads
Review: Everything and More: A Compact History of Infinity (Great Discoveries)
User Review  Oliver Flores  GoodreadsDavid Foster Wallace takes on Aristotle! Well, that's the most that I could really garner from this book, anyway. I'm a huge David Foster Wallace fan, as in DavidFosterWallaceChangedMyLifekind ... Read full review
Review: Everything and More: A Compact History of Infinity (Great Discoveries)
User Review  Jim  Goodreadsa review that I have not read in it's entirety.... http://www.ams.org/notices/200406/rev... and a review I did read that captures the book... http://scienceblogs.com/principles/20... audio of DFW talking about the book https://www.youtube.com/watch?v=Jr4el... Read full review
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abstract actually algebraic analysis Aristotle Aristotle's arithmetic Axiom Axiom of Choice basic bers Bolzano calc calculus Cantor Cantorian cardinal number Cauchy college math concept continuous function Continuum Continuum Hypothesis convergent convergent series correspondence cribbed curve decimal Dedekind defined definition denumerable derived set Dichotomy differential equations Eudoxus example exist finite formal Fourier Series Galileo geometric Georg Cantor Godel going Greek idea important impredicative infi infinite number infinite sequence infinite sets infinitesimals infinity instant integers interval involves irrational numbers kind Kline Kronecker least Leibniz logical math's mathematicians means metaphysical nite Number Line ordertypes ordinal paradoxes Power Set problems proof prove quantities rational numbers Real Line real numbers recall reductio rigorous schnitt semicribbed sense set theory sort specific stuff subsets symbol technical Theorem there's thing tions transfinite transfinite numbers trig series true Weierstrass Weierstrassian whole Zeno Zeno's Zeno's Paradoxes