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The Mathematical Traveler pp 135–159Cite as

Dealing with the Infinite

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Abstract

Any meaningful discussion of numbers must include something on infinity. We have already thrown around the term in exploring the natural number sequence without any attempt to define its meaning. To understand what the natural numbers are is to have a sense for infinity, for understanding numbers implies infinity—that they go on “forever.” Since mathematics begins with the study of numbers, we cannot appreciate either numbers or mathematics without tackling this strange and beautiful idea.

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End Notes

  1. Freeman, p. 14.

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  2. Ibid., p. 19.

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  3. Aristotle, The Basic Works of Aristotle, Physics, Book III, 204b, lines 2–9.

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  4. Freeman, p. 75.

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  5. Aristotle, Physics, Book III, 206b, lines 31–32.

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  6. Ibid., 204b, lines 6–8.

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  7. Ibid., 206a, line 26; 206b, line 13.

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  8. Ibid., 239b, lines 14–18.

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  9. Plato, The Dialogues of Plato, trans. B. Jowett (New York: Random House, 1937), Timeaus, lines 25, 52.

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  10. Rudy Rucker, Infinity and the Mind (New York: Bantam Books, 1982), p. 3.

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  11. Thomas Hobbes, Leviathan: Parts I and II (New York: Bobbs-Merrill Company, 1958), p. 36.

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  12. Thomas Hobbes, “Selections from the De Corpore,” in Philosophers Speak for Themselves: From Descartes to Locke (T. V. Smith and Marjorie Grene, eds.) (Chicago: University of Chicago Press, 1957), p. 144.

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  13. René Descartes, “Meditations on First Philosophy,” in Philosophers Speak for Themselves: From Descartes to Locke, p. 78.

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  14. Hollingdale, p. 359.

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  15. Rucker, p. 88.

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  16. Euclid, Elements, Book III (New York: Dover Publications, 1956), Sec. 14.

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Authors
  1. Calvin C. Clawson
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© 1994 Calvin C. Clawson

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Clawson, C.C. (1994). Dealing with the Infinite. In: The Mathematical Traveler. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6014-6_9

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  • DOI: https://doi.org/10.1007/978-1-4899-6014-6_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-44645-0

  • Online ISBN: 978-1-4899-6014-6

  • eBook Packages: Springer Book Archive

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