# Total order

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 :

- (reflexive).
- If and then (transitive)
- If and then (antisymmetric)
- or (strongly connected, formerly called total).

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Total orders are sometimes also called **simple**,[1] **connex**,[2] or **full orders**.[3]

A set equipped with a total order is a **totally ordered set**;[4] the terms **simply ordered set**,[1] **linearly ordered set**,[2][4] and **loset**[5][6] are also used. The term *chain* is sometimes defined as a synonym of *totally ordered set*,[4] 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.