Dedekind Cut

A set partition of the rational numbers into two nonempty subsets S_1 and S_2 such that all members of S_1 are less than those of S_2 and such that S_1 has no greatest member. Real numbers can be defined using either Dedekind cuts or Cauchy sequences.

See also

Cantor-Dedekind Axiom, Cauchy Sequence

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Courant, 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.

Referenced on Wolfram|Alpha

Dedekind Cut

Cite this as:

Weisstein, Eric W. "Dedekind Cut." From MathWorld--A Wolfram Web Resource.

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