dichotomy

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

The dichotomy between the private and the public is central to almost two centuries of feminist writing and political struggle; it is, ultimately, what the feminist movement is all about. Although some feminists treat the dichotomy as a universal, trans-historical and trans-cultural feature of human existence, feminist criticism is primarily directed at the separation and opposition between the public and private spheres in liberal theory and practice.

The dichotomy between maria and highlands dominates lunar mineralogy.

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

But we do not try to characterize the top and bottom parts of the brain in terms of a simple dichotomy or set of dichotomies, which was exactly what was done with the existing and well-known division of the brain into two halves: namely the left versus the right, the dominant pop-culture brain story of the last few decades. […] The dif­ferences between the left and right sides of the brain are nuanced, and simple, sweeping dichotomies do not in fact explain how the two sides function.

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

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].

The division of a genus into two species; a division into two subordinate parts.

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

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.