dichotomy

1. (logic) The division of a class into two disjoint subclasses that are together comprehensive, as the division of human into female and male.Examples: "But in the fallacy of false dichotomy, not only do the two alternatives fail to be jointly exhaustive, but they are not even likely. As a result, the disjunctive premise is false, or at least probably false."; "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]."countableuncountable

2. (biology, taxonomy) The division of a genus into two species; a division into two subordinate parts.Synonyms: partition, trichotomycountableuncountable

3. (astronomy) A phase of the moon when it appears half lit and half dark, for example at the quadratures.Examples: "The Ides of Januarius indeed, the preceding month, must have fallen on March 1 at midnight, two days before the first dichotomy of the mean new moon of that month, March 3 at midnight."countableuncountable

4. (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.Examples: "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."; "In most of the creeping species with dorsiventral stems (e.g., S. kraussiana, S. laevigata) roots arise at or close to the point of dichotomy; in species like S. rupestris and S. wallichii they arise at the point of dichotomy as well as other positions and in S. selaginoides and S. spinulosa they arise from knot like swellings present at the basal portion of the stem."countableuncountable