(set theory) An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or ⟨a,b⟩.

Having a precise arrangement. / (mathematics, not comparable) Having a well-order.

simple past tense and past participle of well-order

(set theory, order theory, of a set) Equipped with a partial order; when the partial order is specified, often construed with by.

plural of ordered pair

simple past tense and past participle of order out

simple past tense and past participle of mail-order

(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides.

plural of ordered field

simple past tense and past participle of pre-order