Collected works. Vol.4 Continuous geometry and other topics by von Neumann J.

By von Neumann J.

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Infinitesimals from Leibniz to Robinson: time to bring them back to school. Math. Intell. : A History of Mathematics, 3rd edn. : The Nature of Mathematical Knowledge. : Mathematical Thought from Ancient to Modern Times. : Euler and infinite series. Math. Mag. 56, 307–314 (1983) References 47 5 Further Reading 12. : Cavalieri’s method of indivisibles. Arch. Hist. Exact Sci. 31, 291–367 (1985) 13. : The Origins of the Infi nitesimal Calculus. : Differentials, higher-order differentials and the derivative in the Leibnizian calculus.

For example, if there is an unknown number of black and white pebbles in an urn, the probability of drawing a white pebble from the urn can only be determined experimentally—by sampling. Thus, if in n identical trials an event occurs m times, and if n is very large, then m/n should be near the actual—a priori— probability of the event, and should get closer and closer to that probability as n gets larger and larger. See [9] for a precise mathematical statement of Bernoulli’s Law of Large Numbers.

Exact Sci. 14, 1–90 (1974) 15. : Cavalieri, limits and discarded infinitesimals. Scr. Math. 8, 79–91 (1941) 16. : The History of the Calculus and Its Conceptual Development. Dover, New York (1959) 17. : Discussion of fluxions: From Berkeley to Woodhouse. Am. Math. Mon. 24, 145–154 (1917) 18. : Grafting of the theory of limits on the calculus of Leibniz. Am. Math. Mon. 30, 223–234 (1923) 19. : Indivisibles and “ghosts of departed quantities” in the history of mathematics.

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