데데킨트 절단

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  1. To make this more specific, and express it in terms of sets, we define a Dedekind cut to be the left-hand piece in such a division.[1]
  2. We have to say what it means to be a Dedekind cut without referring to a real number that doesn't exist yet.[1]
  3. The three requirements just say, in a mathematically exact way, that a Dedekind cut consists of all rational numbers to the left of some division point.[1]
  4. Each Dedekind cut, that is each possible division point, represents a real number.[1]
  5. and is a Dedekind cut, then pick such that .[2]
  6. A Dedekind cut is, in full clarity, a bounded, open, rounded, located, two-sided Dedekind cut of rational numbers.[2]
  7. A Dedekind cut is a partition of the rational numbers into two 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.[3]
  8. It is straightforward to show that a Dedekind cut among the real numbers is uniquely defined by the corresponding cut among the rational numbers.[3]
  9. The important purpose of the Dedekind cut is to work with number sets that are not complete.[3]
  10. A Dedekind cut is a construction that produces the real numbers from the rational numbers.[4]
  11. To grasp the concept of an irrational number, one really needs the notion of the limit from analysis, or results from higher algebra--the so called " Dedekind cut ".[5]
  12. Since adopting the moniker Dedekind Cut last year, Warmsley has put out three EPs, most recently the cassette American Zen, which comprised four tracks’ worth of even-keeled, dread-tinged drone.[6]
  13. As Dedekind Cut, Warmsley makes use of ambient tropes, but this album’s stakes are set far outside the boundaries of that genre.[6]
  14. A dedekind cut is a natural way to describe sqrt(2).[7]
  15. This means that deriving a Cauchy sequence or decimal expansion from a Dedekind cut in general is just as difficult as solving a general real-valued mathematical problem.[8]
  16. This idea was to figure in Duchamp's final formulation of the nature of the continuum, which involved the elemental parallelism of virtual images, and the concept of the Dedekind cut.[9]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Dedekind Cuts
  2. ↑ 2.0 2.1 Dedekind cut in nLab
  3. ↑ 3.0 3.1 3.2 Dedekind cut
  4. ↑ Dedekind Cut
  5. ↑ Dedekind cut
  6. ↑ 6.0 6.1 Dedekind Cut: $uccessor (ded004)
  7. ↑ Dedekind Cuts
  8. ↑ Difference between constructive Dedekind and Cauchy reals in computation
  9. ↑ Dedekind Cut

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  • [{'LOWER': 'dedekind'}, {'LEMMA': 'cut'}]
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