A dichotomy is any splitting of a whole into exactly two non-overlapping parts, meaning it is a procedure in which a whole is divided into two parts. It is a partition of a whole (or a set) into two parts (subsets) that are:
- jointly exhaustive: everything must belong to one part or the other, and
- mutually exclusive: nothing can belong simultaneously to both parts.
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.
Famous quotes containing the word dichotomy:
“Children’s lives are not shaped solely by their families or immediate surroundings at large. That is why we must avoid the false dichotomy that says only government or only family is responsible. . . . Personal values and national policies must both play a role.”
—Hillary Rodham Clinton (20th century)
“I am a Christian according to my conscience in belief, ... in purpose and wish;Mnot of course by the orthodox standard. But I am content, and have a feeling of trust and safety.
The Machiavellian mind and the merchant mind are at one in their simple faith in the power of segmental division to rule all—in the dichotomy of power and morals and of money and morals.”
—Marshall McLuhan (1911–1980)