Dealing with the Infinite

  • Calvin C. Clawson


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.


Natural Number Infinite Number Number Line North Pole Fibonacci Sequence 
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End Notes

  1. 1.
    Freeman, p. 14.Google Scholar
  2. 2.
    Ibid., p. 19.Google Scholar
  3. 3.
    Aristotle, The Basic Works of Aristotle, Physics, Book III, 204b, lines 2–9.Google Scholar
  4. 4.
    Freeman, p. 75.Google Scholar
  5. 5.
    Aristotle, Physics, Book III, 206b, lines 31–32.Google Scholar
  6. 6.
    Ibid., 204b, lines 6–8.Google Scholar
  7. 7.
    Ibid., 206a, line 26; 206b, line 13.Google Scholar
  8. 8.
    Ibid., 239b, lines 14–18.Google Scholar
  9. 9.
    Plato, The Dialogues of Plato, trans. B. Jowett (New York: Random House, 1937), Timeaus, lines 25, 52.Google Scholar
  10. 10.
    Rudy Rucker, Infinity and the Mind (New York: Bantam Books, 1982), p. 3.MATHGoogle Scholar
  11. 11.
    Thomas Hobbes, Leviathan: Parts I and II (New York: Bobbs-Merrill Company, 1958), p. 36.Google Scholar
  12. 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.Google Scholar
  13. 13.
    René Descartes, “Meditations on First Philosophy,” in Philosophers Speak for Themselves: From Descartes to Locke, p. 78.Google Scholar
  14. 14.
    Hollingdale, p. 359.Google Scholar
  15. 15.
    Rucker, p. 88.Google Scholar
  16. 16.
    Euclid, Elements, Book III (New York: Dover Publications, 1956), Sec. 14.Google Scholar

Copyright information

© Calvin C. Clawson 1994

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  • Calvin C. Clawson

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