A set partition of the rational numbers into two nonempty subsets and such that all members of are less than those of and such that has no greatest member. Real numbers can be defined using either Dedekind cuts or Cauchy sequences.
See alsoCantor-Dedekind Axiom, Cauchy Sequence
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ReferencesCourant, R. and Robbins, H. "Alternative Methods of Defining Irrational Numbers. Dedekind Cuts." §2.2.6 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 71-72, 1996.Jeffreys, H. and Jeffreys, B. S. "Nests of Intervals: Dedekind Section." §1.031 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 6-8, 1988.
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Cite this as:
Weisstein, Eric W. "Dedekind Cut." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DedekindCut.html