simple past tense and past participle of well-order

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

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

(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⟩.

plural of ordered pair

simple past tense and past participle of order up

(set theory, order theory) That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

plural of ordered ring

(algebra, order theory, ring theory) A ring, R, equipped with a partial order, ≤, such that for arbitrary a, b, c ∈ R, if a ≤ b then a + c ≤ b + c, and if, additionally, 0 ≤ c, then both ca ≤ cb and ac ≤ bc.

simple past tense and past participle of mail-order