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Dedekind cut

Dedekind cut noun: any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.

Noun

Dedekind cut (plural Dedekind cuts)

  1. Any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.
    • More than one formal solution was offered; the one which is easiest to work with (all of the solutions are provably equivalent) is the method of Dedekind cuts.1990, Judith Roitman, Introduction to Modern Set Theory, Wiley, page 70
    • To identify Dedekind cuts as the sought-for "real number system," we must show that they include all the rationals and irrationals—all the numbers that can be approximated with arbitrary accuracy by rationals.1997, Reuben Hersh, What is Mathematics, Really?, Oxford University Press, page 274

Dedekind cut meaning in Tamil

Dedekind cut in Tamil

டெடிகின்ட் அமைப்பு

Forms of Dedekind cut

pluralDedekind cuts

Origin of Dedekind cut

Named after German mathematician Richard Dedekind (1831–1916), who introduced the concept (although a similar construction was used in Euclid's Elements to define proportional segments).

Questions about Dedekind cut

What does Dedekind cut mean?
Dedekind cut means any partition of the set of rational numbers into non-empty sets A and B such that all elements of A are less than all elements of B and A contains no greatest element; intended as a construction of a real number.
What is Dedekind cut in Tamil?
Dedekind cut in Tamil is டெடிகின்ட் அமைப்பு. See Dedekind cut meaning in Tamil.
What part of speech is Dedekind cut?
Dedekind cut is a noun.
What is the plural of Dedekind cut?
The plural of Dedekind cut is Dedekind cuts.

Words near Dedekind cut in the dictionary

  1. dedecorous
  2. Dededo
  3. Dedeian
  4. Dedeians
  5. Dedekind
  6. Dedekind cut
  7. Dedekind cuts
  8. Dedekind domain
  9. Dedekind domains
  10. Dedekind ellipsoid
  11. Dedekind ellipsoids

Source and license

Adapted from Wiktionary: Dedekind cut (page history and authors); dedekind cut (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “Dedekind cut.” Word.ws, https://word.ws/dedekind_cut. Based on Wiktionary, CC BY-SA 4.0.