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Index
Cover Title Page Copyright Contents Big numbers Googoled Symbols from India The Book of Calculation 0, a powerful tool Archimedes: The Sand Reckoner The poetry of infinity Number sequences Strange sequences The infinity machine Zeno’s paradoxes Achilles and the tortoise Apeiron Aristotle Potential infinity Left brain/right brain The power of algebra Visual thinking Pythagorean perfection Diagonals of a square Drowning by numbers Squaring the circle Transcendental pi Infinity of pi Omega Not really numbers at all? God and the infinite The human perspective “Only a manner of speaking” Galileo Infinity on wheels Back to geometry The normal rules don’t apply The infinity of 1? A common error The indivisibles Newton and potential infinity Fluxions From o to 0 Leibniz’s calculus Newton vs. Leibniz Notation Differential and integral calculus Battling Bishop Berkeley The infidel mathematician Dividing zero by zero Flow and change Tending towards zero Finding a symbol The Möbius strip and Klein bottle Bolzano and real infinity Cantor: mind-bending infinity The joy of sets Venn diagrams Boolean algebra Making sets of the world Peano and the cardinals Russell’s paradox Cantor and subsets Imaginary numbers Aleph null Cardinals and ordinals Ordinal infinity Countably infinite Cantor’s elegant proof Covering the number line Another Cantor proof Points in space The shock of the infinite Power sets Cantor under attack Cantor succumbs Gödel’s shocking proof Back to the continuum hypothesis Does infinity exist? Fractal infinity Recursion Fractals in nature Measuring the coastline The Cantor set An infinite universe? Edge of the universe? Quantum infinity The slit experiment Spin The infinitesimal Non-standard analysis Infinitesimals and Brownian motion Hilbert’s Hotel Gabriel’s Horn The jungle of infinity Glossary Further Reading Author’s acknowledgements Artist’s acknowledgements About the Authors Index
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