Abstract
We have studied thus far the various kinds of numbers that evolved from the natural numbers: the fractions, negative numbers, and zero. All these numbers together are called rational numbers. Such numbers are familiar to everyone in normal daily activities, from balancing checkbooks to playing blackjack. We are now at the point of learning about kinds of numbers most people are either unaware of, or only encountered years ago in a high school algebra class. Yet, these new numbers are amazing objects that can dazzle and puzzle mathematicians and laymen alike.
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End Notes
A well-ordered set is a simply ordered set such that every subset contains a first element. See Zermelo’s axiom of choice.
Sir Thomas Heath, A History of Greek Mathematics, Vol I (Oxford, England: The Clarendon Press, 1960), p. 385.
The English translation of this work can be found in Richard Dedekind, Essays on the Theory of Numbers (La Salle, IL: Open Court Publishing Company, 1948).
Ibid., p. 6.
Ibid., p. 12.
Ibid., p. 13.
Ibid., p. 15.
Boyer, p. 307.
Ibid., p. 348.
Richard Preston, “Profiles: The Mountains of Pi,” The New Yorker (March 2, 1992), p. 36.
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© 1994 Calvin C. Clawson
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Clawson, C.C. (1994). Dedekind’s Cut. In: The Mathematical Traveler. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6014-6_10
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