Definition of "dichotomy" in Anglais

noun

1. A separation or division into two; a distinction that results in such a division.

2. Such a division involving apparently incompatible or opposite principles; a duality.

3. (logic) The division of a class into two disjoint subclasses that are together comprehensive, as the division of human into female and male.

   • 2011, Tomasz A. Gorarzd, Jacek Krzaczkowski, The Complexity of Problems Connected with Two-Element Algebras, Paweł M. Idziak, Andrzej Wronski, Reports on Mathematical Logic: No. 46, page 92, One can ask if for any algebra the considered problem is always in P or NP-complete (P or coNP-complete)? For example, the problem of the satisfiability of a system of polynomial equations over a group G is in P if G is abelian and NP-complete otherwise ([7, 13]). One of the most widely known subclasses of NP which exhibits such a dichotomy, is the class of constraint satisfaction problems (CSP) on the set {0,1}, see [16]. Recently Bulatov proved the dichotomy for CSP on a three-element set [3].

4. (biology, taxonomy) The division of a genus into two species; a division into two subordinate parts.

5. (astronomy) A phase of the moon when it appears half lit and half dark, for example at the quadratures.

6. (botany) Division and subdivision; bifurcation, such as that of a stem of a plant or a vein of the body into two parts as it proceeds from its origin; often successive.

   • 1969, J. F. Rigby, Permian Sphenopsids from Antarctica, Geological Survey Professional Paper 613-F, page F-9, In one forked leaf there is a distinct vein dichotomy, and the leaf boundary commences 1.5 mm above the dichotomy.