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 :
- If and then (transitive)
- If and then (antisymmetric)
- or (strongly connected, formerly called total).
A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, and loset are also used. The term chain is sometimes defined as a synonym of totally ordered set, but refers generally to some sort of totally ordered subsets of a given partially ordered set.
An extension of a given partial order to a total order is called a linear extension of that partial order.