Dedekind cut


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Related to Dedekind cut: Cauchy sequences

Dedekind cut

(German ˈdedəˌkɪnt)
n
1. (Mathematics) a method of according the same status to irrational and rational numbers, devised by Julius Wilhelm Dedekind (1831-1916)
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
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7 DEDEKIND CUT, AMERICAN ZEN (DED003) (Ninja Tune) Dedekind Cut (formerly Lee Bannon and a collaborator of Joey Bada$$) explores the terrain of subtle ambience--a genre that is generally not considered "Black Music" by any stretch of the term.
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".
(16) A non-empty proper subset C of Q is a (left) Dedekind cut just in case it has no greatest element and is closed under < (i.e., for every a [member of] C, b [member of] C provided that a > b [member of] Q).