simple past tense and past participle of pre-order

(mathematics) A partially ordered set. / (mathematics) A totally ordered set.

(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.

simple past tense and past participle of order out

plural of ordered set

plural of ordered field

(idiomatic) Exactly what is necessary or useful in a given situation; something very beneficial or desirable.

(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order. / (set theory, order theory, formally) The ordered pair comprising a set and its partial order.

(mathematics) An ordered field which satisfies the axiom of Archimedes.

(algebra) An integral domain which has a subset whose elements are said to be "positive", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset.