Abstract
We now approach the proof that ℝ is uncountable. Since the set Q of all rational numbers is countable, it is clear that any valid proof of the uncountability of ℝ must use the continuity of ℝ. The classical formulation of this is as follows.
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© 1982 Springer-Verlag New York, Inc.
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Moise, E.E. (1982). The Completeness of IR. Uncountable Sets. In: Introductory Problem Courses in Analysis and Topology. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8183-9_18
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DOI: https://doi.org/10.1007/978-1-4613-8183-9_18
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