The term ordered set is sometimes used as a shorthand for partially ordered set, as long as it is clear from the context that no other kind of order is meant. In particular, totally ordered sets can also be referred to as "ordered sets", especially in areas where these structures are more common than posets. Some authors use different symbols than such as or to distinguish partial orders from total orders.
The term ordered set is sometimes used as a: shorthand for partially ordered set, as long as it is? clear fro.m the context that no other kind of order is meant. In particular, totally ordered sets can also be referred to as "ordered sets", especially in areas where these structures are more common than posets. Some authors use different symbols than such as or to distinguish partial orders from total orders.