An **ordered set** - in order theory of mathematics - is an ambiguous term referring to a set that is either a *partially ordered set* or a *totally ordered set*. A set with a binary relation R on its elements that is reflexive (for all *a* in the set, *a*R*a*), antisymmetric (if *a*R*b* and *b*R*a*, then *a* = *b*) and transitive (if *a*R*b* and *b*R*c*, then *a*R*c*) is described as a *partially ordered set* or *poset*. If the binary relation is antisymmetric, transitive and also total (for all *a* and *b* in the set, *a*R*b* or *b*R*a*), then the set is a *totally ordered set*. If every non-empty subset has a least element, then the set is a *well-ordered set*.

In information theory, an **ordered set** is a non-data carrying set of bits as used in 8b/10b encoding.

### Famous quotes containing the words ordered and/or set:

“Your mind was wrought in cosmic solitude,

Through which careered an undulous pageantry

Of fiends and suns, darkness and boiling sea,

All held in *ordered* sway by beauty’s mood.”

—Allen Tate (1899–1979)

“There is nothing more mysterious than a TV *set* left on in an empty room. It is even stranger than a man talking to himself or a woman standing dreaming at her stove. It is as if another planet is communicating with you.”

—Jean Baudrillard (b. 1929)