preordered

Preordered is the past participle of preorder and can refer to two distinct concepts in different contexts. In commerce, to preorder an item means to place an order before its official release in order to reserve a copy or guarantee access. Preordered items are common for video games, books, electronics, and limited editions. Retailers may require payment upfront or a deposit, and shipments typically occur on or after the release date. Terms for cancellation and refunds vary by seller and jurisdiction, and prices can change between the time of preorder and release.

In mathematics and logic, preordered describes a set equipped with a preorder relation. A preorder is a binary relation that is reflexive and transitive; a set with such a relation is called a preordered set or a quasiorder. If the preorder is antisymmetric, the structure is a partially ordered set (poset). For example, the natural numbers with the usual ≤ relation form a preorder and, in fact, a poset due to antisymmetry. Preorders are often used to reason about elements up to equivalence, where a is equivalent to b if a ≤ b and b ≤ a.

The term is sometimes distinguished from “order” to emphasize that antisymmetry (and sometimes strictness) may not hold. Quotients of a preordered set by the induced equivalence relation yield a poset, and preorders underpin various constructions in mathematics and computer science where a flexible notion of comparison is useful.