trichotomy UK /tɹaɪˈkɒt.ə.mi/US /tɹaɪˈkɑt.ə.mi/ noun2 •Division or separation into three groups or pieces. •the property of an order relation whereby, given an ordered pair of elements (of a given algebraic structure), exactly one of these is true: the first element is 'less than' the second one, the second is 'less than' the first, or the two elements are equal.[A linear order] obeys the following trichotomy law[.] — 2006 formstrichotomies