Dedekind cut

In mathematics, a Dedekind cut, named after Richard Dedekind, in a totally ordered set S is a partition of it, (A, B), such that A is closed downwards (meaning that for all a in A, x ≤ a implies that x is in A as well) and B is closed upwards, and A contains no greatest element. The cut itself is, conceptually, the "gap" defined between A and B. The original and most important cases are Dedekind cuts for rational numbers and real numbers.

Related Topics:
Mathematics - Richard Dedekind - Totally ordered set - Partition - Rational number - Real number

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