Encyclopedia > Dedekind cut

  Article Content

Dedekind cut

A Dedekind cut in an ordered field is a partition of it, (A, B), such that A is closed downwards (meaning that whenever a is in A and xa, then x is in A as well), B is closed upwards and A has no maximum.

The Dedekind cut is named after Richard Dedekind, who invented this construction in order to represent the real numbers as Dedekind cuts of the rational numbers. A typical Dedekind cut of the rational numbers is given by A = { a in Q : a2 < 2 }, B = { b in Q : b2 ≥ 2 }. This cut represents the real number √ 2 in Dedekind's construction.

this is a stub article

See also:

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Canadian Charter of Rights and Freedoms

... law but also the European Court of Human Rights cases in interpreting the Charter. The Charter limitations clause states: The Canadian Charter of Rights and Freedoms ...

This page was created in 38.8 ms