Summary
We give short proofs that is uncountable directly from the definition of as the set of Dedekind cuts of .
MSC:
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No potential conflict of interest was reported by the author(s).
Notes
1 Another common way to define is as a set of equivalence classes of Cauchy sequences of rationals. The paper by Wenner [Citation5] gives a natural proof that this set of equivalence classes is uncountable.
Additional information
Notes on contributors
David A. Ross
David A. Ross (MR Author ID: 232420) received his Ph.D. from the University of Wisconsin, Madison, and is a professor of mathematics at the University of Hawai‘i at Mānoa. He is interested in most areas of mathematics, but has also published in philosophy, computer science, and zoology. His most enduring legacy will probably be the eponymous ‘droplet technique’ for reducing static in coffee grinding.