In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : 1. * (reflexive). 2. * If and then (transitive). 3. * If and then (antisymmetric). 4. * or (strongly connected, formerly called total). Total orders are sometimes also called simple, connex, or full orders. An extension of a given partial order to a total order is called a linear extension of that partial order.