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6 - ℝ: Real Numbers I, Dedekind Cuts

Published online by Cambridge University Press:  05 December 2024

Edward Scheinerman
Edward Scheinerman
Affiliation:
Johns Hopkins University
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Summary

We define real numbers as equivalence classes of left rays of rational numbers. We show the existence of the square root of 2, and summarize the properties of the real numbers using the concept of a complete ordered field.

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Chapter
Information
From Counting to Continuum
What Are Real Numbers, Really?
 , pp. 81 - 104
Publisher: Cambridge University Press
Print publication year: 2024

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