If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A.
Inset theory, a dichotomous relationR is such that eitheraRb,bRa, but not both.[1]
Afalse dichotomy is aninformal fallacy consisting of a supposed dichotomy which fails one or both of the conditions: it is not jointly exhaustive and/or not mutually exclusive. In its most common form, two entities are presented as if they are exhaustive, when in fact other alternatives are possible. In some cases, they may be presented as if they are mutually exclusive although there is a broad middle ground[2] (see alsoundistributed middle).
One type of dichotomy is dichotomous classification – classifying objects by recursively splitting them into two groups. As Lewis Carroll explains, "After dividing a Class, by the Process of Dichotomy, into two smaller Classes, we may sub-divide each of these into two still smaller Classes; and this Process may be repeated over and over again, the number of Classes being doubled at each repetition. For example, we may divide "books" into "old" and "new" (i.e. "not-old"): we may then sub-divide each of these into "English" and "foreign" (i.e. "not-English"), thus getting four Classes."[3]
Instatistics, dichotomous data may only exist at first twolevels of measurement, namely at thenominal level of measurement (such as "British" vs "American" when measuring nationality) and at theordinal level of measurement (such as "tall" vs "short", when measuring height). A variable measured dichotomously is called adummy variable.
Incomputer science, more specifically in programming-language engineering, dichotomies are fundamental dualities in a language's design. For instance,C++ has a dichotomy in its memory model (heap versus stack), whereas Java has a dichotomy in its type system (references versus primitive data types).
Inastronomy dichotomy is when the Moon or an inferior planet is exactly half-lit as viewed from Earth. For the Moon, this occurs slightly before one quarter Moon orbit and slightly after the third quarter of the Moon's orbit at 89.85° and 270.15°, respectively. (This is not to be confused withquadrature which is when the Sun-Earth-Moon/superior planet angle is 90°.)
Inbotany, branching may be dichotomous oraxillary. In dichotomous branching, the branches form as a result of an equal division of a terminalbud (i.e., a bud formed at the apex of a stem) into two equal branches. This also applies to root systems as well.[4][5]
The dictionary definition ofdichotomy at Wiktionary
