Abstract
In this final chapter we give, in kit form only, two sound constructions of the real numbers ℝ. This takes us back to the spirit of Chapter 1. Recall that we can build ℕ from ø, and that it is an easy step to build ℤ from ℕ. If you have done all the exercises, you will know how to build ℚ from ℤ. We also showed how to construct ℂ from ℝ in Chapter 3. The glaring omission is the construction of ℝ. So far we have relied on our intuition about ℝ. If you want to be sure about the existence and nature of ℝ, read on.
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© 1998 Springer-Verlag London
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Smith, G. (1998). Creating the Real Numbers. In: Introductory Mathematics: Algebra and Analysis. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0619-7_8
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DOI: https://doi.org/10.1007/978-1-4471-0619-7_8
Publisher Name: Springer, London
Print ISBN: 978-3-540-76178-5
Online ISBN: 978-1-4471-0619-7
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