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A dichotomy /daɪˈkɒtəmi/ is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be
- jointly exhaustive: everything must belong to one part or the other, and
- mutually exclusive: nothing can belong simultaneously to both parts.
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.
Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes.