A trichotomous relation on a set $S$ is a relation $R(x, y)$ which satisfies trichotomy:
In classical mathematics, the law of trichotomy or axiom of trichotomy for the real numbers state that the strict total order on the real numbers is trichotomous. In constructive mathematics, this statement is equivalent to the analytic LPO.
In classical mathematics, every strict total order is a trichotomous relation, and strict total orders can be defined as a transitive trichotomous relation. However, in constructive mathematics, only the decidable strict total orders are trichotomous relations.
Last revised on February 22, 2024 at 04:56:06. See the history of this page for a list of all contributions to it.