**Dedekind cut** — Dedekind used his cut to construct the irrational, real numbers. In mathematics, a Dedekind cut, named after Richard Dedekind, is a partition of the rationals into two non empty parts A and B, such that all elements of A are less than all… … Wikipedia

**Dedekind cut** — Math. two nonempty subsets of an ordered field, as the rational numbers, such that one subset is the collection of upper bounds of the second and the second is the collection of lower bounds of the first: can be used to define the real numbers in … Universalium

**Dedekind cut** — Math. two nonempty subsets of an ordered field, as the rational numbers, such that one subset is the collection of upper bounds of the second and the second is the collection of lower bounds of the first: can be used to define the real numbers in … Useful english dictionary

**Cut** — may refer to: The act of cutting, the separation of an object into two through acutely directed force Contents 1 Mathematics 2 Computing 3 … Wikipedia

**Dedekind–MacNeille completion** — The Hasse diagram of a partially ordered set (left) and its Dedekind–MacNeille completion (right). In order theoretic mathematics, the Dedekind–MacNeille completion of a partially ordered set (also called the completion by cuts or normal… … Wikipedia

**Dedekind, Richard** — ▪ German mathematician born Oct. 6, 1831, Braunschweig, duchy of Braunschweig [Germany] died Feb. 12, 1916, Braunschweig German mathematician who developed a major redefinition of irrational numbers (irrational number) in terms of arithmetic… … Universalium

**Dedekind , (Julius Wilhelm) Richard** — (1831–1916) German mathematician The son of an academic lawyer from Braunschweig, Germany, Dedekind was educated at the Caroline College there and at Göttingen, where he gained his doctorate in 1852. After four years spent teaching at Göttingen,… … Scientists

**Richard Dedekind** — Infobox Scientist name = PAGENAME box width = image size =180px caption =Richard Dedekind, c. 1850 birth date = October 6, 1831 birth place = Braunschweig death date = February 12, 1916 death place = Braunschweig residence = citizenship =… … Wikipedia

**0.999...** — In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0 … Wikipedia

**Construction of the real numbers** — In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that … Wikipedia